A387512 a(n) = Sum_{k=0..floor(n/3)} 2^k * 3^(n-2*k) * binomial(n-2*k,k)^2.

1, 3, 9, 33, 153, 729, 3357, 15309, 70713, 331425, 1565325, 7418061, 35250633, 168030369, 803361645, 3850647741, 18495465561, 88998869313, 428955792525, 2070533412333, 10007606103273, 48428342800353, 234607598151597, 1137670448889501, 5521881103615737

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. A387480.

Programs

Magma

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

Mathematica

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

PARI

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

Formula

G.f.: 1/sqrt((1-3*x-6*x^3)^2 - 72*x^4).