A392350 a(n) = Sum_{k=0..floor(3*n/11)} binomial(3*n-10*k,k).

1, 1, 1, 1, 3, 6, 9, 12, 21, 39, 66, 103, 167, 285, 484, 796, 1303, 2167, 3631, 6040, 9988, 16555, 27551, 45838, 76087, 126236, 209685, 348502, 578930, 961269, 1596364, 2651858, 4405203, 7316561, 12151491, 20183152, 33524997, 55684365, 92487340, 153615726

Offset

0,5

Links

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

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

Formula

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

a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) + a(n-4) - a(n-5) + a(n-6) - a(n-7) + a(n-8) - a(n-9) + a(n-10).

Mathematica

CoefficientList[Series[(1-x^4)/(1-x-3*x^4-x^11), {x, 0, 60}], x] (* Vincenzo Librandi, Jan 09 2026 *)

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec((1-x^4)/(1-x-3*x^4-x^11))
(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R! (1 - x^4) / (1 - x - 3*x^4 - x^11)); // Vincenzo Librandi, Jan 09 2026

Crossrefs

Cf. A001018, A033887, A052544, A099234, A190525, A373638, A373718, A392349, A373640, A392351, A392352.

Sequence in context: A203016 A153838 A143829 * A194420 A367952 A277823

Adjacent sequences: A392347 A392348 A392349 * A392351 A392352 A392353

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 07 2026

Status

approved