A392436 a(n) = Sum_{k=0..floor(2*n/7)} binomial(3*k,2*n-7*k).

1, 0, 0, 0, 3, 1, 0, 1, 15, 15, 1, 9, 84, 126, 37, 67, 495, 924, 510, 521, 3004, 6436, 5158, 4425, 18669, 43780, 45088, 38913, 119341, 294359, 363343, 338086, 789762, 1970166, 2785096, 2849288, 5422731, 13199896, 20662701, 23237094, 38486757, 88950636, 149990734

Offset

0,5

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,6,2,0,1,-3,3,-1).

Formula

G.f.: (1 - 3*x^4 - x^5) / (1 - 6*x^4 - 2*x^5 - x^7*(1-x)^3).

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

Mathematica

CoefficientList[Series[(1-3*x^4-x^5)/(1-6*x^4-2*x^5-x^7*(1-x)^3), {x, 0, 40}], x] (* Vincenzo Librandi, Jan 13 2026 *)

Prog

(PARI) my(N=50, x='x+O('x^N)); Vec((1-3*x^4-x^5)/(1-6*x^4-2*x^5-x^7*(1-x)^3))
(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R! (1 - 3*x^4 - x^5) / (1 - 6*x^4 - 2*x^5 - x^7*(1-x)^3)); // Vincenzo Librandi, Jan 13 2026

Crossrefs

Cf. A392431, A375307, A392432, A392433, A392434, A392435.

Sequence in context: A261318 A103879 A322706 * A378761 A051722 A357354

Adjacent sequences: A392433 A392434 A392435 * A392437 A392438 A392439

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 11 2026

Status

approved