A387766 a(n) = Sum_{k=0..floor(n/3)} 2^k * binomial(2*k+1,2*n-6*k).

1, 0, 0, 2, 6, 0, 4, 40, 20, 8, 168, 280, 72, 576, 2016, 1376, 1904, 10560, 14848, 10272, 46112, 109952, 95808, 193024, 641728, 858496, 993664, 3227008, 6312832, 6963200, 15476736, 39087104, 53430528, 81367040, 214845440, 379812352, 507737600, 1124462592

Offset

0,4

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,4,4,0,-4,8,-4).

Formula

G.f.: (1-2*x^3+2*x^4)/((1-2*x^3+2*x^4)^2 - 8*x^4).

a(n) = 4*a(n-3) + 4*a(n-4) - 4*a(n-6) + 8*a(n-7) - 4*a(n-8).

Mathematica

Table[Sum[2^k*Binomial[2*k+1, 2*n-6*k], {k, 0, Floor[n/3]}], {n, 0, 35}] (* Vincenzo Librandi, Sep 12 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\3, 2^k*binomial(2*k+1, 2*n-6*k));
(Magma) [&+[2^k * Binomial(2*k+1, 2*n-6*k): k in [0..Floor(n/3)]]: n in [0..40]]; // Vincenzo Librandi, Sep 12 2025

Crossrefs

Cf. A387764, A387765.

Cf. A387763, A387769.

Sequence in context: A274402 A115252 A108431 * A387479 A390619 A190144

Adjacent sequences: A387763 A387764 A387765 * A387767 A387768 A387769

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 07 2025

Status

approved