A375284 Expansion of (1 - x - x^5)/((1 - x - x^5)^2 - 4*x^6).

1, 1, 1, 1, 1, 2, 7, 16, 29, 46, 68, 107, 191, 364, 686, 1234, 2125, 3596, 6148, 10754, 19132, 34121, 60361, 105725, 184207, 321227, 562628, 989397, 1742190, 3064093, 5377732, 9424960, 16515877, 28964243, 50840968, 89280116, 156762020, 275136201, 482728432

Offset: 0

Author

Seiichi Manyama, Aug 09 2024

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,2,2,0,0,0,-1).

Crossrefs

Cf. A108479, A375279, A375282.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec((1-x-x^5)/((1-x-x^5)^2-4*x^6))

PARI

a(n) = sum(k=0, n\5, binomial(2*n-8*k, 2*k));

Formula

a(n) = 2*a(n-1) - a(n-2) + 2*a(n-5) + 2*a(n-6) - a(n-10).

a(n) = Sum_{k=0..floor(n/5)} binomial(2*n-8*k,2*k).