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

0,4

Links

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

Formula

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

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 *)

Prog

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

Crossrefs

Cf. A387483, A387484.

Sequence in context: A394442 A221655 A221087 * A279580 A197513 A097666

Adjacent sequences: A387482 A387483 A387484 * A387486 A387487 A387488

Keyword

nonn

Author

Seiichi Manyama, Aug 30 2025

Status

approved