A387765 a(n) = Sum_{k=0..floor(n/2)} 2^k * binomial(2*k+1,2*n-4*k).

1, 0, 2, 6, 4, 40, 28, 168, 296, 632, 2048, 3104, 10768, 19776, 51168, 123616, 257344, 693760, 1434304, 3640192, 8267136, 19087232, 46412800, 103556096, 252315904, 575102976, 1357466112, 3190404608, 7363810304, 17495373824, 40378555392, 95234435072, 222133848064

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 - 8*x^3).

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+1, 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+1, 2*n-4*k));
(Magma) [&+[2^k * Binomial(2*k+1, 2*n-4*k): k in [0..Floor(n/2)]]: n in [0..40]]; // Vincenzo Librandi, Sep 12 2025

Crossrefs

Cf. A387764, A387766.

Cf. A387762, A387768.

Sequence in context: A108435 A322827 A322825 * A347555 A215408 A387478

Adjacent sequences: A387762 A387763 A387764 * A387766 A387767 A387768

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 07 2025

Status

approved