A387510 a(n) = Sum_{k=0..floor(n/3)} 2^(n-2*k) * binomial(n-2*k,k)^2.

1, 2, 4, 10, 32, 104, 324, 1000, 3136, 9992, 32064, 103168, 332816, 1077152, 3497024, 11381920, 37121280, 121285760, 396922944, 1300906112, 4269367296, 14028169344, 46143475712, 151932559360, 500710965504, 1651533562368, 5451595506688, 18008220715520

Offset

0,2

Links

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

Formula

G.f.: 1/sqrt((1-2*x-2*x^3)^2 - 16*x^4).

Mathematica

Table[Sum[2^(n-2*k)*Binomial[n-2*k, k]^2, {k, 0, Floor[n/3]}], {n, 0, 30}] (* Vincenzo Librandi, Sep 01 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\3, 2^(n-2*k)*binomial(n-2*k, k)^2);
(Magma) [(&+[2^(n-2*k) * Binomial(n-2*k, k)^2: k in [0..Floor(n/3)]]): n in [0..40]]; // Vincenzo Librandi, Sep 01 2025

Crossrefs

Cf. A387507, A387509.

Cf. A246840, A387513.

Sequence in context: A070900 A296003 A263662 * A151400 A363138 A367113

Adjacent sequences: A387507 A387508 A387509 * A387511 A387512 A387513

Keyword

nonn

Author

Seiichi Manyama, Aug 31 2025

Status

approved