A387516 a(n) = Sum_{k=0..floor(n/3)} 2^(n-3*k) * binomial(k,n-3*k)^2.

1, 0, 0, 1, 2, 0, 1, 8, 4, 1, 18, 36, 9, 32, 144, 129, 66, 400, 801, 472, 932, 3201, 3698, 2916, 9865, 19728, 17248, 28225, 78690, 105536, 106625, 262408, 516388, 566785, 871730, 2064964, 3040713, 3585888, 7366032, 14098817, 17860962, 27066384, 56844833, 88593688

Offset: 0

Author

Seiichi Manyama, Sep 01 2025

Keywords

• nonn
• new

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..2000

Crossrefs

Cf. A387484, A387485.

Cf. A387482.

Programs

Magma

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

Mathematica

Table[Sum[2^(n-3*k)*Binomial[k,n-3*k]^2,{k,0,Floor[n/3]}],{n,0,40}] (* Vincenzo Librandi, Sep 01 2025 *)

PARI

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

Formula

G.f.: 1/sqrt((1-x^3-2*x^4)^2 - 8*x^7).