A387623 a(n) = Sum_{k=0..floor(n/4)} 2^k * binomial(2*n-6*k,2*k).

1, 1, 1, 1, 3, 13, 31, 57, 95, 193, 463, 1081, 2295, 4609, 9423, 20185, 44071, 94801, 199807, 418921, 885879, 1889889, 4034639, 8573561, 18155399, 38461105, 81665695, 173627401, 368961431, 783201921, 1661811055, 3527298329, 7490519335, 15908549329, 33779968447

Offset

0,5

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1500

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,4,4,0,0,-4).

Formula

G.f.: (1-x-2*x^4)/((1-x-2*x^4)^2 - 8*x^5).

a(n) = 2*a(n-1) - a(n-2) + 4*a(n-4) + 4*a(n-5) - 4*a(n-8).

Mathematica

Table[Sum[2^k*Binomial[2*n-6*k, 2*k], {k, 0, Floor[n/4]}], {n, 0, 40}] (* Vincenzo Librandi, Sep 05 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\4, 2^k*binomial(2*n-6*k, 2*k));
(Magma) [&+[2^k* Binomial(2*n-6*k, 2*k): k in [0..Floor (n/4)]]: n in [0..30]]; // Vincenzo Librandi, Sep 05 2025

Crossrefs

Cf. A001541, A108480, A387622.

Cf. A387626, A387629.

Sequence in context: A378946 A145907 A054554 * A051939 A257764 A146728

Adjacent sequences: A387620 A387621 A387622 * A387624 A387625 A387626

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 03 2025

Status

approved