A387485 a(n) = Sum_{k=0..floor(n/3)} 2^(n-2*k) * binomial(k,n-3*k)^2.

1, 0, 0, 2, 4, 0, 4, 32, 16, 8, 144, 288, 80, 512, 2304, 2080, 1856, 12800, 25664, 17408, 58624, 204928, 242944, 299520, 1258752, 2541568, 2609152, 6824448, 20169728, 28344320, 41747456, 132358144, 268472320, 349177856, 807964672, 2116296704, 3336458240

Offset: 0

Author

Seiichi Manyama, Aug 30 2025

Keywords

• nonn
• new

Links

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

Crossrefs

Cf. A387483, A387484.

Programs

Magma

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

Mathematica

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

Formula

G.f.: 1/sqrt((1-2*x^3-4*x^4)^2 - 32*x^7).