A387511 a(n) = Sum_{k=0..floor(n/3)} 3^k * 2^(n-2*k) * binomial(n-2*k,k)^2.

1, 2, 4, 14, 64, 248, 868, 3176, 12352, 48344, 186688, 720896, 2810128, 11021984, 43290688, 170193632, 670576384, 2648370560, 10477291072, 41502538880, 164602863616, 653632824704, 2598446927872, 10339935936512, 41181966803200, 164155849556480, 654848284582912

Offset

0,2

Links

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

Formula

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

Mathematica

Table[Sum[3^k*2^(n-2*k)*Binomial[n-2*k, k]^2, {k, 0, Floor[n/3]}], {n, 0, 30}] (* Vincenzo Librandi, Sep 01 2025 *)

Prog

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

Crossrefs

Cf. A108490.

Sequence in context: A046911 A089127 A132852 * A352644 A389806 A132079

Adjacent sequences: A387508 A387509 A387510 * A387512 A387513 A387514

Keyword

nonn

Author

Seiichi Manyama, Aug 31 2025

Status

approved