Search: a026599 -id:a026599
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A006131
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a(n) = a(n-1) + 4*a(n-2), a(0) = a(1) = 1.
(Formerly M3788)
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+10
46
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1, 1, 5, 9, 29, 65, 181, 441, 1165, 2929, 7589, 19305, 49661, 126881, 325525, 833049, 2135149, 5467345, 14007941, 35877321, 91909085, 235418369, 603054709, 1544728185, 3956947021, 10135859761, 25963647845, 66507086889, 170361678269
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OFFSET
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0,3
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COMMENTS
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Length-n words with letters {0,1,2,3,4} where no two consecutive letters are nonzero, see fxtbook link below. - Joerg Arndt, Apr 08 2011
a(n) is equal to the permanent of the n X n Hessenberg matrix with 1's along the main diagonal, 2's along the superdiagonal and the subdiagonal, and 0's everywhere else. - John M. Campbell, Jun 09 2011
The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n >= 2, 5*a(n-2) equals the number of 5-colored compositions of n with all parts >= 2, such that no adjacent parts have the same color. - Milan Janjic, Nov 26 2011
Pisano period lengths: 1, 1, 8, 1, 6, 8, 48, 2, 24, 6,120, 8, 12, 48, 24, 4,136, 24, 18, 6, ... - R. J. Mathar, Aug 10 2012
This is one of only two Lucas-type sequences whose 8th term is a square. The other one is A097705. - Michel Marcus, Dec 07 2012
Numerators of stationary probabilities for the M2/M/1 queue. In this queue, customers arrives in groups of 2. Intensity of arrival = 1. Service rate = 4. There is only one server and an infinite queue. - Igor Kleiner, Nov 02 2018
Number of 4-compositions of n+2 with 1 not allowed as a part; see Hopkins & Ouvry reference. - Brian Hopkins, Aug 17 2020
a(n) is equal to the number of n-step walks from a universal vertex to another (itself or the other) on the diamond graph. It is also equal to the number of (n+1)-step walks from vertex A to vertex B on the graph below.
B--C
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A--D
(End)
This sequence {a(n-1)}, with a(-1) = 0, appears in the formula for powers of phi17 := (1 + sqrt(17))/2 = A222132, the fundamental (integer) algebraic number of Q(sqrt(17)): phi17^n = A052923(n) + a(n-1)*phi17, for n >= 0.
Limit_{n->oo} a(n+1)/a(n) = phi17. (End)
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Ilya Amburg, Krishna Dasaratha, Laure Flapan, Thomas Garrity, Chansoo Lee, Cornelia Mihaila, Nicholas Neumann-Chun, Sarah Peluse, and Matthew Stoffregen, Stern Sequences for a Family of Multidimensional Continued Fractions: TRIP-Stern Sequences, arXiv:1509.05239 [math.CO], 2015.
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FORMULA
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G.f.: 1/(1 - x - 4*x^2).
a(n) = (((1+sqrt(17))/2)^(n+1) - ((1-sqrt(17))/2)^(n+1))/sqrt(17).
a(n+1) = Sum_{k=0..ceiling(n/2)} 4^k*binomial(n-k, k). - Benoit Cloitre, Mar 06 2004
a(n) = Sum_{k=0..n} binomial((n+k)/2, (n-k)/2)*(1+(-1)^(n-k))*2^(n-k)/2. - Paul Barry, Aug 28 2005
a(n) = Product_{k=1..floor((n - 1)/2)} (1 + 16*cos(k*Pi/n)^2). - Roger L. Bagula, Nov 21 2008
Limiting ratio a(n+1)/a(n) is (1 + sqrt(17))/2 = 2.561552812... - Roger L. Bagula, Nov 21 2008
The fraction b(n) = a(n)/2^n satisfies b(n) = 1/2 b(n-1) + b(n-2); g.f. 1/(1-x/2-x^2); b(n) = (( (1+sqrt(17))/4 )^(n+1) - ( (1-sqrt(17))/4 )^(n+1))*2/sqrt(17). - Franklin T. Adams-Watters, Nov 30 2009
G.f.: G(0)/(2-x), where G(k) = 1 + 1/(1 - x*(17*k-1)/(x*(17*k+16) - 2/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 20 2013
G.f.: Q(0)/2 , where Q(k) = 1 + 1/(1 - x*(4*k+1 + 4*x)/( x*(4*k+3 + 4*x) + 1/Q(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Sep 09 2013
G.f.: Q(0)/2 , where Q(k) = 1 + 1/(1 - x*(k+1 + 4*x)/( x*(k+3/2 + 4*x ) + 1/Q(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Sep 14 2013
G.f.: 1 / (1 - x / (1 - 4*x / (1 + 4*x))). - Michael Somos, Sep 15 2013
a(n) = (Sum_{1<=k<=n+1, k odd} C(n+1,k)*17^((k-1)/2))/2^n. - Vladimir Shevelev, Feb 05 2014
a(n) = 2^n*Fibonacci(n+1, 1/2) = (2/i)^n*ChebyshevU(n, i/4). - G. C. Greubel, Dec 26 2019
E.g.f.: exp(x/2)*(sqrt(17)*cosh(sqrt(17)*x/2) + sinh(sqrt(17)*x/2))/sqrt(17). - Stefano Spezia, Dec 27 2019
With an initial 0 prepended, the sequence [0, 1, 1, 5, 9, 29, 65, ...] satisfies the congruences a(n*p^k) == e*a(n*p^(k-1)) (mod p^k) for positive integers k and n and all primes p, where e = +1 for the primes p listed in A296938, e = 0 when p = 17, otherwise e = -1. - Peter Bala, Dec 28 2022
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EXAMPLE
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G.f. = 1 + x + 5*x^2 + 9*x^3 + 29*x^4 + 65*x^5 + 181*x^6 + 441*x^7 + 1165*x^8 + ...
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MAPLE
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seq( simplify((2/I)^n*ChebyshevU(n, I/4)), n=0..30); # G. C. Greubel, Dec 26 2019
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MATHEMATICA
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m = 16; f[n_] = Product[(1 + m*Cos[k*Pi/n]^2), {k, 1, Floor[(n - 1)/2]}]; Table[FullSimplify[ExpandAll[f[n]]], {n, 0, 15}]; N[%] (* Roger L. Bagula, Nov 21 2008 *)
a[n_]:=(MatrixPower[{{1, 4}, {1, 0}}, n].{{1}, {1}})[[2, 1]]; Table[a[n], {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 19 2010 *)
Table[2^n*Fibonacci[n+1, 1/2], {n, 0, 30}] (* G. C. Greubel, Dec 26 2019 *)
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PROG
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(Sage) [lucas_number1(n, 1, -4) for n in range(1, 30)] # Zerinvary Lajos, Apr 22 2009
(Magma) [ n eq 1 select 1 else n eq 2 select 1 else Self(n-1)+4*Self(n-2): n in [1..40] ]; // Vincenzo Librandi, Aug 19 2011
(PARI) vector(31, n, (2/I)^(n-1)*polchebyshev(n-1, 2, I/4) ) \\ G. C. Greubel, Dec 26 2019
(GAP) a:=[1, 1];; for n in [3..30] do a[n]:=a[n-1]+4*a[n-2]; od; a; # G. C. Greubel, Dec 26 2019
(Python)
list = [1, 1] + [0] * (n - 2)
for i in range(2, n):
list[i] = list[i - 1] + 4 * list[i - 2]
return list
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CROSSREFS
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Cf. A006130, A015440, A026581, A026583, A026597, A026599, A052923, A097705, A102446, A063727, A344236, A344261.
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A026584
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Irregular triangular array T read by rows: T(i,0) = T(i,2i) = 1 for i >= 0; T(i,1) = T(i,2i-1) = floor(i/2) for i >= 1; and for i >= 2 and j = 2..2i-2, T(i,j) = T(i-1,j-2) + T(i-1,j-1) + T(i-1,j) if i+j is odd, and T(i,j) = T(i-1,j-2) + T(i-1,j) if i+j is even.
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+10
26
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1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 1, 4, 2, 4, 1, 1, 1, 2, 5, 7, 8, 7, 5, 2, 1, 1, 2, 8, 9, 20, 14, 20, 9, 8, 2, 1, 1, 3, 9, 19, 28, 43, 40, 43, 28, 19, 9, 3, 1, 1, 3, 13, 22, 56, 62, 111, 86, 111, 62, 56, 22, 13, 3, 1, 1, 4, 14, 38, 69, 140, 167, 259, 222, 259, 167, 140, 69, 38, 14, 4, 1
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OFFSET
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1,7
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COMMENTS
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T(n, k) = number of integer strings s(0)..s(n) such that s(0) = 0, s(n) = n-k, |s(i)-s(i-1)| <= 1 if s(i-1) odd, |s(i)-s(i-1)| = 1 if s(i-1) is even, for i = 1..n.
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LINKS
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FORMULA
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T(n, k) = T(n-1, k-2) + T(n-1, k) if ( (n+k) mod 2 ) = 0, otherwise T(n-1, k-2) + T(n-1, k-1) + T(n-1, k), where T(n, 0) = T(n, 2*n) = 1, T(n, 1) = T(n, 2*n-1) = floor(n/2).
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EXAMPLE
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First 5 rows:
1
1 0 1
1 1 2 1 1
1 1 4 2 4 1 1
1 2 5 7 8 7 5 2 1
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MATHEMATICA
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z = 12; t[n_, 0] := 1; t[n_, k_] := 1 /; k == 2 n; t[n_, 1] := Floor[n/2]; t[n_, k_] := Floor[n/2] /; k == 2 n - 1; t[n_, k_] := t[n, k] = If[EvenQ[n + k], t[n - 1, k - 2] + t[n - 1, k], t[n - 1, k - 2] + t[n - 1, k - 1] + t[n - 1, k]]; u = Table[t[n, k], {n, 0, z}, {k, 0, 2 n}];
v = Flatten[u] (* A026584 sequence *)
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PROG
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(Sage)
@CachedFunction
def T(n, k):
if (k==0 or k==2*n): return 1
elif (k==1 or k==2*n-1): return (n//2)
else: return T(n-1, k-2) + T(n-1, k) if ((n+k)%2==0) else T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
flatten([[T(n, k) for k in (0..2*n)] for n in (0..12)]) # G. C. Greubel, Dec 11 2021
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CROSSREFS
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Cf. A026585, A026587, A026589, A026590, A026591, A026592, A026593, A026594, A026595, A026596, A026597, A026598, A026599.
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KEYWORD
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nonn,tabf
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A026585
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a(n) = T(n,n), T given by A026584. Also a(n) is the number of integer strings s(0), ..., s(n) counted by T, such that s(n)=0.
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+10
21
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1, 0, 2, 2, 8, 14, 40, 86, 222, 518, 1296, 3130, 7770, 19066, 47324, 117094, 291260, 724302, 1806220, 4507230, 11266718, 28188070, 70609316, 177023466, 444231564, 1115639586, 2803975860, 7052132546, 17748069294, 44693162266
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OFFSET
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0,3
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COMMENTS
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The signed sequence 1,0,2,-2,8,-14,... is the inverse binomial transform of A026569. - Paul Barry, Sep 09 2004
Hankel transform of a(n) is 2^n. Hankel transform of a(n+1) is {0, -4, 0, 16, 0, -64, 0, 256, 0, ...} or -2^(n+1)*[x^n](x/(1+x^2)). Hankel transform of a(n+2) is 2^(n+1)*A109613(n+1). - Paul Barry, Mar 23 2011
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LINKS
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FORMULA
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G.f.: 1/(1 -2*x^2/(1 -x -x^2/(1 -x^2/(1 -x -x^2/(1 -x^2/(1 -x -x^2/(1 - ... (continued fraction).
a(0) = 1, a(n) = Sum_{k=0..floor(n/2)} (k/(n-k))*C(n-k,k)*A000984(k). (End)
a(n) = Sum_{k=0..floor(n/2)} C(n-k-1,n-2*k)*A000984(k).
a(n) = Sum_{k=0..floor(n/2)} C(n-k-1,n-2*k)*C(2*k,k). (End)
D-finite with recurrence n*a(n) +2*(-n+1)*a(n-1) +(-3*n+2)*a(n-2) +2*(2*n-5)*a(n-3) = 0. - R. J. Mathar, Nov 24 2012
a(n) ~ (sqrt(17)+1)^(n-1/2) / (17^(1/4) * sqrt(Pi*n) * 2^(n-3/2)). - Vaclav Kotesovec, Feb 12 2014
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MATHEMATICA
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CoefficientList[Series[Sqrt[(1-x)/(1-x-4*x^2)], {x, 0, 40}], x] (* Vaclav Kotesovec, Feb 12 2014 *)
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PROG
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(Magma) [(&+[Binomial(n-j-1, n-2*j)*Binomial(2*j, j): j in [0..Floor(n/2)]]): n in [0..40]]; // G. C. Greubel, Dec 12 2021
(Sage) [sum(binomial(n-j-1, n-2*j)*binomial(2*j, j) for j in (0..(n//2))) for n in [0..40]] # G. C. Greubel, Dec 12 2021
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CROSSREFS
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Cf. A026584, A026587, A026589, A026590, A026591, A026592, A026593, A026594, A026595, A026596, A026597, A026598, A026599, A027282, A027283, A027284, A027285, A027286.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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1, 1, 1, 1, 5, 8, 19, 22, 69, 121, 341, 406, 1203, 2155, 6336, 7624, 22593, 40717, 121483, 147001, 438533, 792351, 2381512, 2892044, 8677763, 15703156, 47419503, 57728737, 173984792, 315180458, 954961034, 1164727748, 3522101709
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OFFSET
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0,5
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LINKS
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FORMULA
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MATHEMATICA
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T[n_, k_]:= T[n, k]= If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[n/2], If[EvenQ[n+k], T[n-1, k-2] + T[n-1, k], T[n-1, k-2] + T[n-1, k-1] + T[n-1, k] ]]]; (* T = A026584 *)
Table[T[n, Floor[n/2]], {n, 0, 40}] (* G. C. Greubel, Dec 13 2021 *)
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PROG
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(Sage)
@CachedFunction
if (k==0 or k==2*n): return 1
elif (k==1 or k==2*n-1): return (n//2)
else: return T(n-1, k-2) + T(n-1, k) if ((n+k)%2==0) else T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
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CROSSREFS
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Cf. A026584, A026585, A026587, A026589, A026590, A026591, A026592, A026593, A026594, A026596, A026597, A026598, A026599, A027282, A027283, A027284, A027285, A027286.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A026587
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a(n) = T(n, n-2), T given by A026584. Also a(n) = number of integer strings s(0),...,s(n) counted by T, such that s(n)=2.
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+10
17
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1, 1, 5, 9, 28, 62, 167, 399, 1024, 2518, 6359, 15819, 39759, 99427, 249699, 626203, 1573524, 3953446, 9943905, 25019005, 62994733, 158680545, 399936573, 1008438757, 2543992514, 6420413940, 16210331727, 40943722115, 103453402718
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OFFSET
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2,3
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LINKS
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FORMULA
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Conjecture: (n+2)*a(n) = (3*n+2)*a(n-1) +(3*n+2)*a(n-2) -(11*n-16)*a(n-3) -2*(n-3)*a(n-4) +4*(2*n-9)*a(n-5). - R. J. Mathar, Jun 23 2013
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MATHEMATICA
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T[n_, k_]:= T[n, k]= If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[n/2], If[EvenQ[n+k], T[n-1, k-2] + T[n-1, k], T[n-1, k-2] + T[n-1, k-1] + T[n-1, k] ]]]; (* T = A026584 *)
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PROG
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(Sage)
@CachedFunction
if (k==0 or k==2*n): return 1
elif (k==1 or k==2*n-1): return (n//2)
else: return T(n-1, k-2) + T(n-1, k) if ((n+k)%2==0) else T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
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CROSSREFS
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Cf. A026584, A026585, A026589, A026590, A026591, A026592, A026593, A026594, A026595, A026596, A026597, A026598, A026599, A027282, A027283, A027284, A027285, A027286.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A026589
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a(n) = T(n,n-4), T given by A026584. Also a(n) = number of integer strings s(0),...,s(n) counted by T, such that s(n)=4.
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+10
17
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1, 2, 9, 22, 69, 178, 497, 1294, 3452, 8964, 23430, 60556, 156663, 403214, 1037191, 2660978, 6821200, 17459732, 44657246, 114117628, 291449047, 743904326, 1897956899, 4840429962, 12340947855, 31455453822, 80158533099
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OFFSET
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4,2
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LINKS
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FORMULA
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Conjecture: -(n+4)*(65*n-269)*a(n) +(-65*n^2+140*n+1933)*a(n-1) +(809*n^2-2431*n-4514)*a(n-2) +(-123*n^2+2496*n-205)*a(n-3) +2*(-726*n^2+3737*n-4395)*a(n-4) +8*(56*n-215)*(2*n-9)*a(n-5) = 0. - R. J. Mathar, Jun 23 2013
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MATHEMATICA
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T[n_, k_]:= T[n, k]= If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[n/2], If[EvenQ[n+k], T[n-1, k-2] + T[n-1, k], T[n-1, k-2] + T[n-1, k-1] + T[n-1, k] ]]]; (* T = A026584 *)
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PROG
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(Sage)
@CachedFunction
if (k==0 or k==2*n): return 1
elif (k==1 or k==2*n-1): return (n//2)
else: return T(n-1, k-2) + T(n-1, k) if ((n+k)%2==0) else T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
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CROSSREFS
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Cf. A026584, A026585, A026587, A026590, A026591, A026592, A026593, A026594, A026595, A026596, A026597, A026598, A026599, A027282, A027283, A027284, A027285, A027286.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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1, 1, 5, 19, 69, 341, 1203, 6336, 22593, 121483, 438533, 2381512, 8677763, 47419503, 173984792, 954961034, 3522101709, 19397198595, 71831252031, 396646918211, 1473610012405, 8154682794333, 30376120747792, 168394714422722, 628648474795879, 3490216221862041, 13053833414221023, 72566287730964469
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OFFSET
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0,3
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LINKS
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FORMULA
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MATHEMATICA
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T[n_, k_]:= T[n, k]= If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[n/2], If[EvenQ[n+k], T[n-1, k-2] + T[n-1, k], T[n-1, k-2] + T[n-1, k-1] + T[n-1, k] ]]]; (* T = A026584 *)
a[n_]:= a[n]= Block[{$RecursionLimit= Infinity}, T[2*n, n]];
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PROG
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(Sage)
@CachedFunction
if (k==0 or k==2*n): return 1
elif (k==1 or k==2*n-1): return (n//2)
else: return T(n-1, k-2) + T(n-1, k) if ((n+k)%2==0) else T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
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CROSSREFS
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Cf. A026584, A026585, A026587, A026589, A026591, A026592, A026593, A026594, A026595, A026596, A026597, A026598, A026599, A027282, A027283, A027284, A027285, A027286.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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1, 2, 9, 38, 140, 701, 2534, 13294, 48369, 258430, 947694, 5114572, 18872399, 102539204, 380143356, 2075658454, 7723000261, 42330184638, 157951859953, 868376395790, 3247811317907, 17899895038348, 67075896452000, 370442993383238, 1390392820937920, 7692166179956366, 28910883325637649, 160184255555687056
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OFFSET
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1,2
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LINKS
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FORMULA
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MATHEMATICA
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T[n_, k_]:= T[n, k]= If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[n/2], If[EvenQ[n+k], T[n-1, k-2] + T[n-1, k], T[n-1, k-2] + T[n-1, k-1] + T[n-1, k] ]]]; (* T = A026584 *)
a[n_]:= a[n]= Block[{$RecursionLimit= Infinity}, T[2*n, n-1]];
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PROG
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(Sage)
@CachedFunction
if (k==0 or k==2*n): return 1
elif (k==1 or k==2*n-1): return (n//2)
else: return T(n-1, k-2) + T(n-1, k) if ((n+k)%2==0) else T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
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CROSSREFS
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Cf. A026584, A026585, A026587, A026589, A026590, A026592, A026593, A026594, A026595, A026596, A026597, A026598, A026599, A027282, A027283, A027284, A027285, A027286.
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KEYWORD
|
nonn
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|
AUTHOR
|
|
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EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|
|
|
|
1, 3, 14, 65, 251, 1288, 4830, 25518, 95388, 510532, 1910821, 10309234, 38656462, 209766714, 787912030, 4294635438, 16155375825, 88371236851, 332859949946, 1826080683788, 6885797551334, 37867515477338, 142929375411104, 787637258527505, 2975423924172735, 16425495119248041, 62096233990615140, 343318987947145114
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
|
2,2
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LINKS
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FORMULA
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MATHEMATICA
|
T[n_, k_]:= T[n, k]= If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[n/2], If[EvenQ[n+k], T[n-1, k-2] + T[n-1, k], T[n-1, k-2] + T[n-1, k-1] + T[n-1, k] ]]]; (* T = A026584 *)
a[n_]:= a[n]= Block[{$RecursionLimit= Infinity}, T[2*n, n-2]];
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PROG
|
(Sage)
@CachedFunction
if (k==0 or k==2*n): return 1
elif (k==1 or k==2*n-1): return (n//2)
else: return T(n-1, k-2) + T(n-1, k) if ((n+k)%2==0) else T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
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CROSSREFS
|
Cf. A026584, A026585, A026587, A026589, A026590, A026591, A026593, A026594, A026595, A026596, A026597, A026598, A026599, A027282, A027283, A027284, A027285, A027286.
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KEYWORD
|
nonn
|
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AUTHOR
|
|
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EXTENSIONS
|
|
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STATUS
|
approved
|
|
|
|
|
|
|
1, 1, 8, 22, 121, 406, 2155, 7624, 40717, 147001, 792351, 2892044, 15703156, 57728737, 315180458, 1164727748, 6385672193, 23691834033, 130316812494, 485018155062, 2674846358141, 9980763478121, 55161813337474, 206262229900060, 1142020843590221, 4277853480389546, 23721423518350124, 88991782850212510
(list;
graph;
refs;
listen;
history;
text;
internal format)
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|
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OFFSET
|
1,3
|
|
LINKS
|
|
|
FORMULA
|
|
|
MATHEMATICA
|
T[n_, k_]:= T[n, k]= If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[n/2], If[EvenQ[n+k], T[n-1, k-2] + T[n-1, k], T[n-1, k-2] + T[n-1, k-1] + T[n-1, k] ]]]; (* T = A026584 *)
a[n_]:= a[n]= Block[{$RecursionLimit= Infinity}, T[2*n-1, n-1]];
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PROG
|
(Sage)
@CachedFunction
if (k==0 or k==2*n): return 1
elif (k==1 or k==2*n-1): return (n//2)
else: return T(n-1, k-2) + T(n-1, k) if ((n+k)%2==0) else T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
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CROSSREFS
|
Cf. A026584, A026585, A026587, A026589, A026590, A026591, A026592, A026594, A026595, A026596, A026597, A026598, A026599, A027282, A027283, A027284, A027285, A027286.
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KEYWORD
|
nonn
|
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AUTHOR
|
|
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EXTENSIONS
|
|
|
STATUS
|
approved
|
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