A387478 a(n) = Sum_{k=0..floor(n/2)} 2^k * 3^(n-2*k) * binomial(k,n-2*k)^2.

1, 0, 2, 6, 4, 48, 44, 216, 664, 984, 5216, 9312, 30160, 93312, 194528, 717792, 1674688, 4842624, 14554304, 35517312, 112151680, 293213568, 823387136, 2409934848, 6348908800, 18760218624, 51418362368, 143838905856, 414017065984, 1132211048448, 3255687793664

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

G.f.: 1/sqrt((1-2*x^2-6*x^3)^2 - 48*x^5).

Mathematica

Table[Sum[2^k* 3^(n-2*k)*Binomial[k, n-2*k]^2, {k, 0, Floor[n/2]}], {n, 0, 40}] (* Vincenzo Librandi, Sep 01 2025 *)

Prog

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

Crossrefs

Cf. A108490, A387479.

Sequence in context: A387765 A347555 A215408 * A264609 A126262 A330078

Adjacent sequences: A387475 A387476 A387477 * A387479 A387480 A387481

Keyword

nonn

Author

Seiichi Manyama, Aug 30 2025

Status

approved