A387763 a(n) = Sum_{k=0..floor(n/3)} 2^k * binomial(2*k,2*n-6*k).

1, 0, 0, 2, 2, 0, 4, 24, 4, 8, 120, 120, 24, 448, 1120, 480, 1456, 6720, 6784, 5664, 31712, 59264, 43328, 132352, 384704, 415104, 594048, 2062208, 3373184, 3616768, 9971712, 22629376, 27365632, 49197056, 131033088, 204249600, 281805312, 695709696, 1372816384

Offset

0,4

Links

Seiichi Manyama, 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 - 16*x^7).

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, 2*n-6*k], {k, 0, Floor[n/3]}], {n, 0, 40}] (* Vincenzo Librandi, Sep 12 2025 *)

Prog

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

Crossrefs

Cf. A108485, A387762.

Cf. A387648.

Sequence in context: A052079 A387477 A390695 * A291483 A181295 A166299

Adjacent sequences: A387760 A387761 A387762 * A387764 A387765 A387766

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 07 2025

Status

approved