A390222 a(n) = Sum_{k=0..floor(n/2)} binomial(k+2,4*n-8*k+2).

1, 0, 3, 0, 6, 0, 10, 0, 15, 1, 21, 7, 28, 28, 36, 84, 45, 210, 56, 462, 77, 924, 144, 1716, 377, 3003, 1106, 5006, 3123, 8023, 8144, 12496, 19601, 19244, 43929, 30192, 92569, 50388, 184985, 93024, 353137, 190893, 648229, 420717, 1151657, 951787, 1995205, 2138379

Offset

0,3

Links

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

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

Formula

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

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

a(n) = A390040(n) - A390040(n-2).

Mathematica

CoefficientList[Series[(1-x^2)/((1-x^2)^4-x^9), {x, 0, 50}], x] (* Vincenzo Librandi, Jan 20 2026 *)

Prog

(PARI) my(N=50, x='x+O('x^N)); Vec((1-x^2)/((1-x^2)^4-x^9))
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R! (1-x^2) / ((1-x^2)^4 - x^9)); // Vincenzo Librandi, Jan 20 2026

Crossrefs

Cf. A390040, A390220, A390221.

Sequence in context: A115456 A328788 A007386 * A007385 A390035 A390219

Adjacent sequences: A390219 A390220 A390221 * A390223 A390224 A390225

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 19 2026

Status

approved