A390042 a(n) = Sum_{k=0..floor(n/3)} binomial(k+3,4*n-12*k+3).

1, 0, 0, 4, 0, 0, 10, 0, 0, 20, 0, 0, 35, 1, 0, 56, 8, 0, 84, 36, 0, 120, 120, 0, 165, 330, 1, 220, 792, 12, 286, 1716, 78, 364, 3432, 364, 455, 6435, 1365, 561, 11440, 4368, 696, 19448, 12376, 952, 31824, 31824, 1785, 50388, 75582, 5016, 77521, 167960, 16834, 116300

Offset

0,4

Links

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

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

Formula

G.f.: 1 / ((1-x^3)^4 - x^13).

a(n) = 4*a(n-3) - 6*a(n-6) + 4*a(n-9) - a(n-12) + a(n-13).

Mathematica

CoefficientList[Series[1/((1-x^3)^4-x^13), {x, 0, 60}], x] (* Vincenzo Librandi, Jan 16 2026 *)

Prog

(PARI) my(N=60, x='x+O('x^N)); Vec(1/((1-x^3)^4-x^13))
(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R! 1 / ((1-x^3)^4 - x^13)); // Vincenzo Librandi, Jan 16 2026

Crossrefs

Cf. A390040.

Sequence in context: A244121 A127774 A127319 * A390041 A272626 A271910

Adjacent sequences: A390039 A390040 A390041 * A390043 A390044 A390045

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 14 2026

Status

approved