OFFSET
1,1
REFERENCES
D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.4.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
Beate Bollig, Martin Löbbing, Martin Sauerhoff and Ingo Werner, On the complexity of the hidden weighted bit function for various BDD models, Theoretical Informatics and Applications, 33 (1999), 103-115, Theorem 4.4.
Randal E. Bryant, On the complexity of VLSI implementations and graph representations of Boolean functions with application to integer multiplication, IEEE Transactions on Computers C-40 (1991), 205-213.
Index entries for linear recurrences with constant coefficients, signature (1,2,0,-3,-2,2,2,0,-1).
FORMULA
a(n) = (56*P(n+2)+77*P(n+1)+47*P(n))/23 - floor(n^2/4) - floor((7*n+1)/3) + (n mod 2) - 10, where P = A001608. - Don Knuth, Dec 09 2008
G.f.: -x*(x^8+x^7-2*x^6-3*x^5-2*x^4+3*x^3+2*x^2-3) / ((x-1)^3*(x+1)*(x^2+x+1)*(x^3+x^2-1)). - Colin Barker, Jan 29 2013
EXAMPLE
By the first formula: a(9) = (56*A001608(11)+77*A001608(10) + 47*A001608(9))/23 - floor(9^2/4) - floor((7*9+1)/3) + (9 mod 2) - 10 = 135 - 20 - 21 + 1 - 10 = 85. - Bruno Berselli, Jan 31 2013
MATHEMATICA
p[n_] := n*Sum[Binomial[k, n-2*k]/k, {k, 1, n/2}]; a[n_] := (56*p[n+2] + 77*p[n+1] + 47*p[n])/23 - Floor[n^2/4] - Floor[(7*n+1)/3] + Mod[n, 2] - 10; Table[a[n], {n, 1, 41}] (* Jean-François Alcover, Jan 31 2013 *)
LinearRecurrence[{1, 2, 0, -3, -2, 2, 2, 0, -1}, {3, 3, 7, 10, 17, 25, 40, 57, 85}, 50] (* Vincenzo Librandi, Aug 09 2015 *)
PROG
(Magma) I:=[3, 3, 7, 10, 17, 25, 40, 57, 85]; [n le 9 select I[n] else Self(n-1)+2*Self(n-2)-3*Self(n-4)-2*Self(n-5)+2*Self(n-6)+2*Self(n-7)-Self(n-9): n in [1..45]]; // Vincenzo Librandi, Aug 09 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Don Knuth, Apr 04 2008
STATUS
approved