A070832 a(n) = Sum_{k=0..n} binomial(8*n,8*k).

1, 2, 12872, 1470944, 622116992, 125858012672, 36758056208384, 8793364151263232, 2334899414608412672, 586347560750962049024, 151652224498623981289472, 38612725801339748322639872, 9913426188311626771400228864

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

Sum_{k=0..n} binomial(b*n,b*k): A000079 (b=1), A081294 (b=2), A007613 (b=3), A070775 (b=4), A070782 (b=5), A070967 (b=6), A094211 (b=7), this sequence (b=8), A094213 (b=9), A070833 (b=10).

Sequence in context: A265013 A083973 A094212 * A170994 A151599 A297573

Adjacent sequences: A070829 A070830 A070831 * A070833 A070834 A070835

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