A387762 a(n) = Sum_{k=0..floor(n/2)} 2^k * binomial(2*k,2*n-4*k).

1, 0, 2, 2, 4, 24, 12, 120, 136, 456, 1152, 1888, 6800, 10944, 33248, 70816, 160064, 419328, 850880, 2256512, 4874112, 11749504, 27833344, 62598144, 153483520, 344694784, 827492864, 1917989376, 4464268288, 10580625408, 24362683392, 57748781056, 133950105600

Offset

0,3

Links

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

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

Formula

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

a(n) = 4*a(n-2) + 4*a(n-3) - 4*a(n-4) + 8*a(n-5) - 4*a(n-6).

Mathematica

Table[Sum[2^k*Binomial[2*k, 2*n-4*k], {k, 0, Floor[n/2]}], {n, 0, 35}] (* Vincenzo Librandi, Sep 12 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\2, 2^k*binomial(2*k, 2*n-4*k));
(Magma) [&+[2^k * Binomial(2*k, 2*n-4*k): k in [0..Floor(n/2)]]: n in [0..40]]; // Vincenzo Librandi, Sep 12 2025

Crossrefs

Cf. A108485, A387763.

Sequence in context: A270527 A232275 A257612 * A009541 A307969 A212672

Adjacent sequences: A387759 A387760 A387761 * A387763 A387764 A387765

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 07 2025

Status

approved