A387647 a(n) = Sum_{k=0..floor(n/2)} 2^(n-2*k) * binomial(2*k,2*n-4*k).

1, 0, 1, 2, 1, 12, 5, 30, 61, 64, 281, 314, 857, 1812, 2701, 7606, 11925, 26376, 55393, 96402, 223985, 405276, 835989, 1726158, 3233133, 6901328, 13260073, 26731882, 54453001, 105630628, 217246237, 427776358, 856449221, 1729791512, 3411468145, 6904065986

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1500

Index entries for linear recurrences with constant coefficients, signature (0,2,4,-1,4,-4).

Formula

G.f.: (1-x^2-2*x^3)/((1-x^2-2*x^3)^2 - 8*x^5).

a(n) = 2*a(n-2) + 4*a(n-3) - a(n-4) + 4*a(n-5) - 4*a(n-6).

Mathematica

Table[Sum[2^(n-2*k)*Binomial[2*k, 2*n-4*k], {k, 0, Floor[n/2]}], {n, 0, 40}] (* Vincenzo Librandi, Sep 06 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\2, 2^(n-2*k)*binomial(2*k, 2*n-4*k));
(Magma) [&+[2^(n-2*k)* Binomial(2*k, 2*n-4*k): k in [0..Floor (n/2)]]: n in [0..40]]; // Vincenzo Librandi, Sep 06 2025

Crossrefs

Cf. A108480, A387648.

Sequence in context: A370552 A167128 A332749 * A342430 A181417 A048743

Adjacent sequences: A387644 A387645 A387646 * A387648 A387649 A387650

Keyword

nonn

Author

Seiichi Manyama, Sep 04 2025

Status

approved