A392351 a(n) = Sum_{k=0..floor(3*n/14)} binomial(3*n-13*k,k).

1, 1, 1, 1, 1, 3, 6, 9, 12, 15, 24, 42, 69, 105, 151, 224, 351, 559, 875, 1331, 2009, 3071, 4760, 7400, 11417, 17486, 26768, 41153, 63504, 97979, 150788, 231651, 355985, 547828, 843774, 1299209, 1998922, 3074277, 4729178, 7277986, 11202381, 17240300, 26526635

Offset

0,6

Links

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

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,3,0,0,0,0,0,0,0,0,1).

Formula

G.f.: (1 - x^5) / (1 - x - 3*x^5 - x^14).

a(n) = a(n-1) + 3*a(n-5) + a(n-14).

Mathematica

CoefficientList[Series[(1-x^5)/(1-x-3*x^5-x^14), {x, 0, 60}], x] (* Vincenzo Librandi, Jan 09 2026 *)

Prog

(PARI) my(N=50, x='x+O('x^N)); Vec((1-x^5)/(1-x-3*x^5-x^14))
(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R! (1 - x^5) / (1 - x - 3*x^5 - x^14)); // Vincenzo Librandi, Jan 09 2026

Crossrefs

Cf. A001018, A033887, A052544, A099234, A190525, A373638, A373718, A392349, A373640, A392350, A392352.

Sequence in context: A371000 A184999 A289761 * A310151 A310152 A189783

Adjacent sequences: A392348 A392349 A392350 * A392352 A392353 A392354

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 07 2026

Status

approved