Revision History for A026598
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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#11 by Joerg Arndt at Wed Dec 15 01:18:49 EST 2021
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#10 by Michel Marcus at Wed Dec 15 00:32:27 EST 2021
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#9 by G. C. Greubel at Wed Dec 15 00:29:28 EST 2021
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#8 by G. C. Greubel at Wed Dec 15 00:26:36 EST 2021
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| NAME
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Sum{Ta(n) = Sum_{i,j)}, =0<=..n} Sum_{j<=i, =0<=..i} T(i<=n, ,j), T given by A026584.
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| LINKS
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G. C. Greubel, <a href="/A026598/b026598.txt">Table of n, a(n) for n = 0..500</a>
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| FORMULA
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a(n) = Sum_{i=0..n} Sum_{j=0..i} A026584(i, j).
Conjecture: n*a(n) +(-) - (4*n+-3)*a(n-1) +(-) - (2*n+-3)*a(n-2) +) + 5*(4*n-9)*a(n-3) +) - 7*(-*(n+-3)*a(n-4) +) - 6*(-*(4*n+-15)*a(n-5) +) + 8*(2*n-9)*a(n-6)=) = 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, 0, 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] ]]]];
a[n_]:= a[n]= Block[{$RecursionLimit = Infinity}, Sum[T[i, j], {i, 0, n}, {j, 0, i}]];
Table[a[n], {n, 0, 40}] (* G. C. Greubel, Dec 15 2021 *)
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| PROG
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(Sage)
@CachedFunction
def T(n, k): # T = A026584
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)
@CachedFunction
def A026598(n): return sum(sum(T(i, j) for j in (0..i)) for i in (0..n))
[A026598(n) for n in (0..40)] # G. C. Greubel, Dec 15 2021
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| CROSSREFS
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Cf. A026584, A026585, A026587, A026589, A026590, A026591, A026592, A026593, A026594, A026595, A026596, A026597, A026599, A027282, A027283, A027284, A027285, A027286.
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| STATUS
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approved
editing
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#7 by R. J. Mathar at Sun Jun 23 12:53:12 EDT 2013
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#6 by R. J. Mathar at Sun Jun 23 12:13:16 EDT 2013
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| FORMULA
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Conjecture: n*a(n) +(-4*n+3)*a(n-1) +(-2*n+3)*a(n-2) +5*(4*n-9)*a(n-3) +7*(-n+3)*a(n-4) +6*(-4*n+15)*a(n-5) +8*(2*n-9)*a(n-6)=0. - R. J. Mathar, Jun 23 2013
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| STATUS
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approved
editing
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#5 by Russ Cox at Fri Mar 30 18:56:09 EDT 2012
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Discussion
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| Fri Mar 30
| 18:56
| OEIS Server: https://oeis.org/edit/global/285
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#4 by N. J. A. Sloane at Sun Feb 20 03:00:00 EST 2005
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| NAME
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SUMSum{T(i,j)}, 0<=j<=i, 0<=i<=n, T given by A026584.
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| KEYWORD
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nonn,new
nonn
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#3 by N. J. A. Sloane at Sat Sep 13 03:00:00 EDT 2003
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| KEYWORD
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nonn,new
nonn
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| AUTHOR
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Clark Kimberling, (ck6(AT)evansville.edu)
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#2 by N. J. A. Sloane at Fri May 16 03:00:00 EDT 2003
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| KEYWORD
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nonn,new
nonn
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| AUTHOR
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Clark Kimberling, ck6@cedar.(AT)evansville.edu
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