A387768 a(n) = Sum_{k=0..floor(n/2)} 2^k * binomial(2*k+1,2*n-4*k+1).

1, 0, 6, 2, 20, 40, 60, 280, 312, 1352, 2368, 5856, 15632, 28864, 86048, 168096, 434496, 1002752, 2234560, 5649536, 12211840, 30328960, 68791296, 161430528, 383891712, 874668032, 2099908096, 4817531392, 11379016704, 26596497408, 61848337408, 145932523520

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,4,4,-4,8,-4).

Formula

G.f.: (1+2*x^2-2*x^3)/((1+2*x^2-2*x^3)^2 - 8*x^2).

a(n) = 4*a(n-2) + 4*a(n-3) - 4*a(n-4) + 8*a(n-5) - 4*a(n-6).

Mathematica

Table[Sum[2^k*Binomial[2*k+1, 2*n-4*k+1], {k, 0, Floor[n/2]}], {n, 0, 30}] (* Vincenzo Librandi, Sep 26 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\2, 2^k*binomial(2*k+1, 2*n-4*k+1));
(Magma) [&+[2^k*Binomial(2*k+1, 2*n-4*k+1): k in [0..Floor(n/2)]]: n in [0..30]]; // Vincenzo Librandi, Sep 26 2025

Crossrefs

Cf. A387767, A387769.

Sequence in context: A277275 A213503 A169632 * A201445 A090033 A036173

Adjacent sequences: A387765 A387766 A387767 * A387769 A387770 A387771

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 07 2025

Status

approved