A392356 a(n) = Sum_{k=0..floor(5*n/9)} binomial(k,5*n-9*k).

1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 6, 1, 21, 1, 56, 1, 126, 2, 252, 12, 462, 67, 792, 287, 1287, 1002, 2003, 3004, 3019, 8009, 4504, 19449, 7004, 43759, 12444, 92380, 27132, 184778, 69768, 352948, 190893, 648418, 516648, 1154693, 1341154, 2014387, 3311290

Offset

0,12

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,5,0,-10,0,10,0,-5,1,1).

Formula

G.f.: (1-x^2)^4 / ((1-x^2)^5 - x^9).

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

Mathematica

CoefficientList[Series[(1-x^2)^4/((1-x^2)^5-x^9), {x, 0, 60}], x] (* Vincenzo Librandi, Jan 08 2026 *)

Prog

(PARI) my(N=50, x='x+O('x^N)); Vec((1-x^2)^4/((1-x^2)^5-x^9))
(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1-x^2)^4 / ((1-x^2)^5 - x^9)); // Vincenzo Librandi, Jan 08 2026

Crossrefs

Cf. A392271, A392355.

Sequence in context: A387649 A096130 A120666 * A050300 A185678 A286893

Adjacent sequences: A392353 A392354 A392355 * A392357 A392358 A392359

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 08 2026

Status

approved