A390041 a(n) = Sum_{k=0..floor(4*n/11)} binomial(k+3,4*n-11*k).

1, 0, 0, 4, 0, 0, 10, 0, 0, 20, 0, 1, 35, 0, 8, 56, 0, 36, 84, 0, 120, 120, 1, 330, 165, 12, 792, 220, 78, 1716, 286, 364, 3432, 365, 1365, 6435, 471, 4368, 11440, 696, 12376, 19448, 1496, 31824, 31825, 4692, 75582, 50408, 16473, 167960, 77730, 55404, 352716

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,-6,0,0,4,0,1,-1).

Formula

G.f.: 1 / ((1-x^3)^4 - x^11).

a(n) = 4*a(n-3) - 6*a(n-6) + 4*a(n-9) + a(n-11) - a(n-12).

Mathematica

CoefficientList[Series[1/((1-x^3)^4-x^11), {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^11))
(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R! 1 / ((1-x^3)^4 - x^11)); // Vincenzo Librandi, Jan 16 2026

Crossrefs

Cf. A390039.

Sequence in context: A127774 A127319 A390042 * A272626 A271910 A249346

Adjacent sequences: A390038 A390039 A390040 * A390042 A390043 A390044

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 14 2026

Status

approved