A392454 a(n) = Sum_{k=0..floor(2*n/3)} binomial(2*k+1,2*n-3*k).

1, 0, 3, 2, 10, 12, 36, 57, 138, 250, 549, 1060, 2227, 4427, 9120, 18364, 37513, 75949, 154603, 313701, 637699, 1295022, 2631240, 5344988, 10858285, 22058847, 44810670, 91034937, 184929945, 375691009, 763192224, 1550434777, 3149634952, 6398479259, 12998281146

Offset

0,3

Links

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

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

Formula

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

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

Mathematica

CoefficientList[Series[(1-x^2+x^3)/(1-4*x^2-x^3*(1-x)^2), {x, 0, 60}], x] (* Vincenzo Librandi, Jan 14 2026 *)

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec((1-x^2+x^3)/(1-4*x^2-x^3*(1-x)^2))
(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!  (1 - x^2 + x^3) / (1 - 4*x^2 - x^3*(1-x)^2)); // Vincenzo Librandi, Jan 14 2026

Crossrefs

Cf. A376716, A376787, A392455, A376788, A392456.

Cf. A392428.

Sequence in context: A019242 A064367 A113980 * A095675 A340806 A226442

Adjacent sequences: A392451 A392452 A392453 * A392455 A392456 A392457

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 13 2026

Status

approved