A387509 a(n) = Sum_{k=0..floor(n/3)} 2^(n-k) * binomial(n-2*k,k)^2.

1, 2, 4, 12, 48, 176, 592, 2016, 7168, 25920, 93440, 336384, 1216768, 4425216, 16143360, 58993664, 215965696, 792154112, 2910720000, 10710884352, 39464009728, 145575002112, 537583419392, 1987177611264, 7352243781632, 27224715689984, 100888181211136

Offset: 0

Author

Seiichi Manyama, Aug 31 2025

Keywords

• nonn
• new

Links

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

Crossrefs

Cf. A375276.

Programs

Magma

[(&+[2^(n-k) * Binomial(n-2*k, k)^2: k in [0..Floor(n/3)]]): n in [0..40]]; // Vincenzo Librandi, Sep 02 2025

Mathematica

Table[Sum[2^(n-k)*Binomial[n-2*k,k]^2,{k,0,Floor[n/3]}],{n,0,30}] (* Vincenzo Librandi, Sep 02 2025 *)

PARI

a(n) = sum(k=0, n\3, 2^(n-k)*binomial(n-2*k, k)^2);

Formula

G.f.: 1/sqrt((1-2*x-4*x^3)^2 - 32*x^4).