A375291 Expansion of (1 - x + x^4)/((1 - x + x^4)^2 + 4*x^5).

1, 1, 1, 1, 0, -5, -14, -27, -43, -50, -20, 91, 342, 784, 1380, 1861, 1519, -1025, -7877, -21302, -41829, -64128, -70003, -19381, 155984, 544288, 1208731, 2073244, 2706380, 2003100, -2136215, -12820099, -33219215, -63581579, -94886444, -98351925, -12445158

Offset

0,6

Links

Table of n, a(n) for n=0..36.

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

Prog

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

Crossrefs

Cf. A375289.

Sequence in context: A185233 A065351 A002503 * A014106 A110325 A331775

Adjacent sequences: A375288 A375289 A375290 * A375292 A375293 A375294

Keyword

sign

Author

Seiichi Manyama, Aug 10 2024

Status

approved