OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..664
Index entries for linear recurrences with constant coefficients, signature (21,353,-32).
FORMULA
a(n) = (1/5)*32^n + (2/5)*(-11/2 + (5/2)*sqrt(5))^n + (2/5)*(-11/2 - (5/2)*sqrt(5))^n.
Let b(n) = a(n) - 2^(5n)/5; then b(n) + 11*b(n-1) - b(n-2) = 0. - Benoit Cloitre, May 27 2004
From Colin Barker, May 27 2019: (Start)
G.f.: (1 - 19*x - 141*x^2) / ((1 - 32*x)*(1 + 11*x - x^2)).
a(n) = 21*a(n-1) + 353*a(n-2) - 32*a(n-3) for n>2.
(End)
MATHEMATICA
LinearRecurrence[{21, 353, -32}, {1, 2, 254}, 20] (* Harvey P. Dale, Jun 18 2023 *)
PROG
(PARI) a(n)=sum(k=0, n, binomial(5*n, 5*k))
(PARI) Vec((1 - 19*x - 141*x^2) / ((1 - 32*x)*(1 + 11*x - x^2)) + O(x^20)) \\ Colin Barker, May 27 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Sebastian Gutierrez and Sarah Kolitz (skolitz(AT)mit.edu), May 15 2002
STATUS
approved