A392267 a(n) = Sum_{k=0..floor(2*n/3)} (k+1) * binomial(k,2*n-3*k).

1, 0, 2, 3, 3, 12, 9, 30, 35, 67, 111, 161, 296, 420, 728, 1103, 1764, 2802, 4313, 6897, 10588, 16691, 25830, 40137, 62365, 96225, 149235, 229840, 354936, 546400, 840653, 1292760, 1984226, 3045967, 4668159, 7152380, 10947997, 16746318, 25601471, 39107943

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,4,2,-6,-4,3,2,-1).

Formula

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

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

Mathematica

CoefficientList[Series[((1-x^2)^2+x^3)/((1-x^2)^2-x^3)^2, {x, 0, 60}], x] (* Vincenzo Librandi, Jan 16 2026 *)

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(((1-x^2)^2+x^3)/((1-x^2)^2-x^3)^2)
(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R! ((1-x^2)^2 + x^3) / ((1-x^2)^2 - x^3)^2); // Vincenzo Librandi, Jan 16 2026

Crossrefs

Cf. A391962, A392251, A392268.

Sequence in context: A161960 A287428 A232933 * A303700 A196837 A275212

Adjacent sequences: A392264 A392265 A392266 * A392268 A392269 A392270

Keyword

nonn

Author

Seiichi Manyama, Jan 05 2026

Status

approved