A387477 a(n) = Sum_{k=0..floor(n/3)} 2^k * binomial(k,n-3*k)^2.

1, 0, 0, 2, 2, 0, 4, 16, 4, 8, 72, 72, 24, 256, 576, 288, 816, 3200, 3264, 3104, 14432, 25728, 20672, 58752, 157120, 173184, 257152, 809600, 1296000, 1466368, 3814400, 8247296, 10202368, 18360320, 46069760, 71264768, 100919808, 238362624, 457049088, 635490304

Offset

0,4

Links

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

Formula

G.f.: 1/sqrt((1-2*x^3-2*x^4)^2 - 16*x^7).

D-finite with recurrence n*a(n) +2*(-2*n+3)*a(n-3) +4*(-n+2)*a(n-4) +4*(n-3)*a(n-6) +4*(-2*n+7)*a(n-7) +4*(n-4)*a(n-8)=0. - R. J. Mathar, Sep 07 2025

Mathematica

Table[Sum[2^k*Binomial[k, n-3*k]^2, {k, 0, Floor[n/3]}], {n, 0, 40}] (* Vincenzo Librandi, Aug 31 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\3, 2^k*binomial(k, n-3*k)^2);
(Magma) [(&+[2^k * Binomial(k, n-3*k)^2: k in [0..Floor(n/3)]]): n in [0..40]]; // Vincenzo Librandi, Aug 31 2025

Crossrefs

Cf. A375276, A387476.

Sequence in context: A151868 A344913 A052079 * A390695 A387763 A291483

Adjacent sequences: A387474 A387475 A387476 * A387478 A387479 A387480

Keyword

nonn

Author

Seiichi Manyama, Aug 30 2025

Status

approved