A392250 a(n) = Sum_{k=0..floor(n/2)} binomial(k,2*(n-2*k)).

1, 0, 1, 0, 1, 1, 1, 3, 1, 6, 2, 10, 6, 15, 16, 22, 36, 35, 71, 64, 128, 129, 220, 265, 376, 529, 661, 1013, 1211, 1873, 2290, 3394, 4382, 6126, 8347, 11148, 15706, 20552, 29191, 38303, 53824, 71760, 99009, 134408, 182497, 250880, 337745, 466361, 627401, 864339

Offset

0,8

Links

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

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

Formula

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

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

a(2*n) = A005676(n), a(2*n+1) = A385142(n+2).

Mathematica

CoefficientList[Series[(1-x^2)/((1-x^2)^2-x^5), {x, 0, 50}], x] (* Vincenzo Librandi, Jan 06 2026 *)

Prog

(PARI) my(A=1, B=1, C=A^2*B, N=1, M=50, x='x+O('x^M), X=1-A*x^2, Y=5); Vec(sum(k=0, N\2, C^k*binomial(N, 2*k)*X^(N-2*k)*x^(Y*k))/(X^2-C*x^Y)^N)
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1-x^2) / ((1-x^2)^2 - x^5)); // Vincenzo Librandi, Jan 06 2026

Crossrefs

Cf. A005251, A062200, A391265, A391399.

Cf. A392251, A392252.

Cf. A005676, A385142.

Sequence in context: A386947 A105358 A240691 * A322387 A336173 A072361

Adjacent sequences: A392247 A392248 A392249 * A392251 A392252 A392253

Keyword

nonn

Author

Seiichi Manyama, Jan 04 2026

Status

approved