A387476 a(n) = Sum_{k=0..floor(n/2)} 2^k * binomial(k,n-2*k)^2.

1, 0, 2, 2, 4, 16, 12, 72, 88, 264, 608, 1056, 3280, 5504, 15328, 31904, 71104, 175488, 358080, 900736, 1925248, 4518016, 10404864, 23138304, 54970624, 122038272, 286077440, 651510272, 1492685824, 3465687040, 7876488192, 18322630656, 41904609280, 96788580352, 223335882752

Offset

0,3

Links

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

Formula

G.f.: 1/sqrt((1-2*x^2-2*x^3)^2 - 16*x^5).

D-finite with recurrence n*a(n) +4*(-n+1)*a(n-2) +2*(-2*n+3)*a(n-3) +4*(n-2)*a(n-4) +4*(-2*n+5)*a(n-5) +4*(n-3)*a(n-6)=0. - R. J. Mathar, Sep 07 2025

Mathematica

Table[Sum[2^k* Binomial[k, n-2*k]^2, {k, 0, Floor[n/2]}], {n, 0, 40}] (* Vincenzo Librandi, Aug 31 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\2, 2^k*binomial(k, n-2*k)^2);
(Magma) [(&+[2^k * Binomial(k, n-2*k)^2: k in [0..Floor(n/2)]]): n in [0..40]]; // Vincenzo Librandi, Aug 31 2025

Crossrefs

Cf. A375276, A387477.

Cf. A052907.

Sequence in context: A106241 A395972 A392124 * A153991 A153994 A102864

Adjacent sequences: A387473 A387474 A387475 * A387477 A387478 A387479

Keyword

nonn

Author

Seiichi Manyama, Aug 30 2025

Status

approved