A387477 a(n) = Sum_{k=0..floor(n/3)} 2^k * binomial(k,n-3*k)^2.

1, 0, 0, 2, 2, 0, 4, 16, 4, 8, 72, 72, 24, 256, 576, 288, 816, 3200, 3264, 3104, 14432, 25728, 20672, 58752, 157120, 173184, 257152, 809600, 1296000, 1466368, 3814400, 8247296, 10202368, 18360320, 46069760, 71264768, 100919808, 238362624, 457049088, 635490304

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. A375276, A387476.

Programs

Magma

[(&+[2^k * Binomial(k,n-3*k)^2: k in [0..Floor(n/3)]]): n in [0..40]]; // Vincenzo Librandi, Aug 31 2025

Mathematica

Table[Sum[2^k*Binomial[k,n-3*k]^2,{k,0,Floor[n/3]}],{n,0,40}] (* Vincenzo Librandi, Aug 31 2025 *)

PARI

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

Formula

G.f.: 1/sqrt((1-2*x^3-2*x^4)^2 - 16*x^7).