A392435 a(n) = Sum_{k=0..floor(n/3)} binomial(3*k,2*n-6*k).

1, 0, 0, 1, 3, 0, 1, 15, 15, 2, 36, 126, 85, 75, 495, 925, 600, 1431, 5007, 6588, 6063, 19020, 43983, 49743, 72829, 206826, 363495, 428528, 852102, 1999155, 3001497, 4181787, 9199161, 18112232, 25922379, 43124106, 92287620, 160195491, 238123350, 443261263

Offset

0,5

Links

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

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

Formula

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

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

Mathematica

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

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec((1-x^3-3*x^4)/(1-2*x^3-6*x^4+x^6*(1-x)^3))
(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!  (1 - x^3 - 3*x^4) / (1 - 2*x^3 - 6*x^4 + x^6*(1-x)^3)); // Vincenzo Librandi, Jan 13 2026

Crossrefs

Cf. A392431, A375307, A392432, A392433, A392434, A392436.

Sequence in context: A334823 A279031 A304336 * A287315 A350212 A256311

Adjacent sequences: A392432 A392433 A392434 * A392436 A392437 A392438

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 11 2026

Status

approved