A392268 a(n) = Sum_{k=0..floor(2*n/5)} (k+1) * binomial(k,2*n-5*k).

1, 0, 0, 2, 0, 3, 3, 0, 12, 4, 5, 30, 5, 30, 60, 13, 105, 105, 63, 280, 177, 260, 630, 342, 849, 1271, 855, 2320, 2442, 2475, 5568, 4818, 7095, 12206, 10439, 18891, 25402, 25025, 46377, 52339, 63080, 106365, 111035, 158282, 232710, 247555, 383911, 497760, 575881, 893622

Offset

0,4

Links

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

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

Formula

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

a(n) = 4*a(n-3) + 2*a(n-5) - 6*a(n-6) - 4*a(n-8) + 4*a(n-9) - a(n-10) + 2*a(n-11) - a(n-12).

Mathematica

CoefficientList[Series[((1-x^3)^2+x^5)/((1-x^3)^2-x^5)^2, {x, 0, 60}], x] (* Vincenzo Librandi, Jan 16 2026 *)

Prog

(PARI) my(N=50, x='x+O('x^N)); Vec(((1-x^3)^2+x^5)/((1-x^3)^2-x^5)^2)
(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R! ((1-x^3)^2 + x^5) / ((1-x^3)^2 - x^5)^2); // Vincenzo Librandi, Jan 16 2026

Crossrefs

Cf. A391962, A392251, A392267.

Sequence in context: A298605 A180013 A377657 * A094067 A094112 A333303

Adjacent sequences: A392265 A392266 A392267 * A392269 A392270 A392271

Keyword

nonn

Author

Seiichi Manyama, Jan 05 2026

Status

approved