A375283 Expansion of 1/((1 - x - x^4)^2 - 4*x^5).

1, 2, 3, 4, 7, 16, 35, 68, 122, 220, 417, 816, 1588, 3028, 5707, 10784, 20547, 39322, 75150, 143144, 272212, 517990, 987005, 1881824, 3586808, 6832874, 13013780, 24789200, 47229672, 89991518, 171459667, 326651952, 622295173, 1185547900, 2258689217, 4303264572

Offset

0,2

Links

Table of n, a(n) for n=0..35.

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

Formula

a(n) = 2*a(n-1) - a(n-2) + 2*a(n-4) + 2*a(n-5) - a(n-8).

a(n) = (1/2) * Sum_{k=0..floor(n/4)} binomial(2*n-6*k+2,2*k+1).

Prog

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

Crossrefs

Cf. A182890, A375278, A375285.

Cf. A246883, A375282.

Sequence in context: A254432 A027362 A068194 * A179985 A338928 A110705

Adjacent sequences: A375280 A375281 A375282 * A375284 A375285 A375286

Keyword

nonn

Author

Seiichi Manyama, Aug 09 2024

Status

approved