A390040 a(n) = Sum_{k=0..floor(n/2)} binomial(k+3,4*n-8*k+3).

1, 0, 4, 0, 10, 0, 20, 0, 35, 1, 56, 8, 84, 36, 120, 120, 165, 330, 221, 792, 298, 1716, 442, 3432, 819, 6435, 1925, 11441, 5048, 19464, 13192, 31960, 32793, 51204, 76722, 81396, 169291, 131784, 354276, 224808, 707413, 415701, 1355642, 836418, 2507299

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,4,0,-6,0,4,0,-1,1).

Formula

G.f.: 1 / ((1-x^2)^4 - x^9).

a(n) = 4*a(n-2) - 6*a(n-4) + 4*a(n-6) - a(n-8) + a(n-9).

Mathematica

CoefficientList[Series[1/((1-x^2)^4-x^9), {x, 0, 60}], x] (* Vincenzo Librandi, Jan 16 2026 *)

Prog

(PARI) my(N=50, x='x+O('x^N)); Vec(1/((1-x^2)^4-x^9))
(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R! 1 / ((1-x^2)^4 - x^9)); // Vincenzo Librandi, Jan 16 2026

Crossrefs

Cf. A390042.

Sequence in context: A184363 A331451 A390323 * A164735 A390039 A382522

Adjacent sequences: A390037 A390038 A390039 * A390041 A390042 A390043

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 14 2026

Status

approved