A387479 a(n) = Sum_{k=0..floor(n/3)} 2^k * 3^(n-3*k) * binomial(k,n-3*k)^2.

1, 0, 0, 2, 6, 0, 4, 48, 36, 8, 216, 648, 232, 768, 5184, 6944, 3696, 28800, 86464, 71712, 137376, 691328, 1185216, 1067904, 4280512, 12749952, 15523200, 26248832, 102010752, 201056256, 243856384, 694548480, 1995570432, 3031771136, 5109762048, 16129681920

Offset

0,4

Links

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

Formula

G.f.: 1/sqrt((1-2*x^3-6*x^4)^2 - 48*x^7).

Mathematica

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

Crossrefs

Cf. A108490, A387478.

Sequence in context: A115252 A108431 A387766 * A390619 A190144 A019967

Adjacent sequences: A387476 A387477 A387478 * A387480 A387481 A387482

Keyword

nonn

Author

Seiichi Manyama, Aug 30 2025

Status

approved