A392455 a(n) = Sum_{k=0..floor(2*n/5)} binomial(2*k+1,2*n-5*k).

1, 0, 0, 3, 1, 1, 10, 5, 7, 35, 22, 37, 126, 95, 174, 463, 408, 770, 1732, 1742, 3290, 6584, 7385, 13760, 25384, 31078, 56786, 99043, 129886, 232393, 390242, 539558, 946121, 1549554, 2229896, 3839826, 6189683, 9176831, 15556174, 24835641, 37636912, 62964623

Offset

0,4

Links

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

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

Formula

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

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

Mathematica

CoefficientList[Series[(1-x^3+x^4)/(1-4*x^3-x^5*(1-x)^2), {x, 0, 60}], x] (* Vincenzo Librandi, Jan 14 2026 *)

Prog

(PARI) my(N=50, x='x+O('x^N)); Vec((1-x^3+x^4)/(1-4*x^3-x^5*(1-x)^2))
(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!  (1 - x^3 + x^4) / (1 - 4*x^3 - x^5*(1-x)^2)); // Vincenzo Librandi, Jan 14 2026

Crossrefs

Cf. A376716, A392454, A376787, A376788, A392456.

Cf. A392429.

Sequence in context: A263864 A060543 A267751 * A185996 A261215 A176157

Adjacent sequences: A392452 A392453 A392454 * A392456 A392457 A392458

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 13 2026

Status

approved