OFFSET
0,4
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,5)
FORMULA
G.f.: (1-2*x+x^2)/(1-3*x+3*x^2-5*x^3).
a(n) = 3*a(n-1) - 3*a(n-2) + 5*a(n-3).
a(n) = Sum_{k=0..floor(n/3)} binomial(n, 3k) * 4^k.
MATHEMATICA
LinearRecurrence[{3, -3, 5}, {1, 1, 1}, 30] (* Amiram Eldar, Oct 11 2021 *)
CoefficientList[Series[(1-x)^2/((1-x)^3-4x^3), {x, 0, 30}], x] (* Harvey P. Dale, May 06 2022 *)
PROG
(PARI) a(n) = sum(k=0, n\3, binomial(n, 3*k) * 4^k); \\ Michel Marcus, Oct 11 2021
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jul 25 2004
STATUS
approved