A392271 a(n) = Sum_{k=0..floor(3*n/5)} binomial(k,3*n-5*k).

1, 0, 1, 0, 1, 1, 1, 4, 1, 10, 2, 20, 8, 35, 29, 57, 85, 94, 211, 175, 464, 385, 938, 935, 1808, 2289, 3459, 5385, 6826, 12031, 14198, 25686, 30960, 53176, 69143, 108699, 154433, 223215, 340006, 465867, 734561, 991088, 1561313, 2138884, 3286129, 4643816, 6900097, 10067197

Offset

0,8

Links

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

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

Formula

G.f.: (1-x^2)^2 / ((1-x^2)^3 - x^5).

a(n) = 3*a(n-2) - 3*a(n-4) + a(n-5) + a(n-6).

a(2*n) = A107025(n), a(2*n+1) = A373963(n+1).

Mathematica

CoefficientList[Series[(1-x^2)^2/((1-x^2)^3-x^5), {x, 0, 60}], x] (* Vincenzo Librandi, Jan 07 2026 *)

Prog

(PARI) my(N=50, x='x+O('x^N)); Vec((1-x^2)^2/((1-x^2)^3-x^5))
(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1-x^2)^2 / ((1-x^2)^3 - x^5)); // Vincenzo Librandi, Jan 07 2026

Crossrefs

Cf. A003522, A392253, A392272, A392273.

Cf. A017837, A107025, A373963.

Sequence in context: A347115 A381055 A006370 * A262370 A108759 A158824

Adjacent sequences: A392268 A392269 A392270 * A392272 A392273 A392274

Keyword

nonn

Author

Seiichi Manyama, Jan 05 2026

Status

approved