OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..332
Index entries for linear recurrences with constant coefficients, signature (522,587797,-75135226,-392963125,3200000).
FORMULA
a(n) = 1/10*1024^n+1/5*(-625/2+275/2*sqrt(5))^n+1/5*(-625/2-275/2*sqrt(5))^n+1/5*(123/2+55/2*sqrt(5))^n+1/5*(123/2-55/2*sqrt(5))^n.
G.f.: (1 - 520*x - 404083*x^2 + 37605988*x^3 + 117888625*x^4 - 320000*x^5) / ((1 - 1024*x)*(1 - 123*x + x^2)*(1 + 625*x + 3125*x^2)). - Colin Barker, Mar 15 2019
a(2*n) = (2^(20*n-1) + Lucas(20*n) + 5^(5*n)*Lucas(10*n))/5, for n>0 and for Lucas(n) = A000032(n). - Greg Dresden, Feb 04 2023
PROG
(PARI) a(n) = sum(k=0, n, binomial(10*n, 10*k)); \\ Michel Marcus, Mar 15 2019
(PARI) Vec((1 - 520*x - 404083*x^2 + 37605988*x^3 + 117888625*x^4 - 320000*x^5) / ((1 - 1024*x)*(1 - 123*x + x^2)*(1 + 625*x + 3125*x^2)) + O(x^15)) \\ Colin Barker, Mar 15 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Sebastian Gutierrez and Sarah Kolitz (skolitz(AT)mit.edu), May 15 2002
STATUS
approved