A387511 a(n) = Sum_{k=0..floor(n/3)} 3^k * 2^(n-2*k) * binomial(n-2*k,k)^2.

1, 2, 4, 14, 64, 248, 868, 3176, 12352, 48344, 186688, 720896, 2810128, 11021984, 43290688, 170193632, 670576384, 2648370560, 10477291072, 41502538880, 164602863616, 653632824704, 2598446927872, 10339935936512, 41181966803200, 164155849556480, 654848284582912

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. A108490.

Programs

Magma

[(&+[3^k * 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

Mathematica

Table[Sum[3^k*2^(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, 3^k*2^(n-2*k)*binomial(n-2*k, k)^2);

Formula

G.f.: 1/sqrt((1-2*x-6*x^3)^2 - 48*x^4).