A375285 Expansion of 1/((1 - x - x^5)^2 - 4*x^6).

1, 2, 3, 4, 5, 8, 17, 36, 69, 120, 196, 320, 547, 980, 1786, 3216, 5661, 9804, 16932, 29472, 51820, 91602, 161767, 284424, 498103, 871150, 1525380, 2676544, 4703158, 8265354, 14514236, 25464576, 44656997, 78324398, 137430720, 241225072, 423451668, 743244866

Offset

0,2

Links

Table of n, a(n) for n=0..37.

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,2,2,0,0,0,-1).

Formula

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

a(n) = (1/2) * Sum_{k=0..floor(n/5)} binomial(2*n-8*k+2,2*k+1).

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(1/((1-x-x^5)^2-4*x^6))
(PARI) a(n) = sum(k=0, n\5, binomial(2*n-8*k+2, 2*k+1))/2;

Crossrefs

Cf. A182890, A375278, A375283.

Cf. A246884.

Sequence in context: A337280 A081711 A055638 * A057657 A293591 A116657

Adjacent sequences: A375282 A375283 A375284 * A375286 A375287 A375288

Keyword

nonn

Author

Seiichi Manyama, Aug 09 2024

Status

approved