OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..415
Index entries for linear recurrences with constant coefficients, signature (136,32880,-552704,-65536).
FORMULA
Let b(n) = a(n)-2^(8*n)/8 then b(n)+120*b(n-1)-2160*b(n-2)-256*b(n-3)=0. - Benoit Cloitre, May 27 2004
a(n) = 1/4*16^n + 1/8*256^n + 1/4*(-68 + 48*sqrt(2))^n + 1/4*(-68-48*sqrt(2))^n.
From Colin Barker, May 27 2019: (Start)
G.f.: (1 - 134*x - 20280*x^2 + 207296*x^3 + 8192*x^4) / ((1 - 16*x)*(1 - 256*x)*(1 + 136*x + 16*x^2)).
a(n) = 21*a(n-1) + 353*a(n-2) - 32*a(n-3) for n>4.
(End)
MATHEMATICA
Table[Sum[Binomial[8n, 8k], {k, 0, n}], {n, 0, 15}] (* Harvey P. Dale, Nov 25 2020 *)
PROG
(PARI) a(n)=sum(k=0, n, binomial(8*n, 8*k)); \\ Benoit Cloitre, May 27 2004
(PARI) Vec((1 - 134*x - 20280*x^2 + 207296*x^3 + 8192*x^4) / ((1 - 16*x)*(1 - 256*x)*(1 + 136*x + 16*x^2)) + O(x^15)) \\ Colin Barker, May 27 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Sebastian Gutierrez and Sarah Kolitz (skolitz(AT)mit.edu), May 15 2002
EXTENSIONS
Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 15 2007
STATUS
approved