A387626 a(n) = Sum_{k=0..floor(n/4)} 2^k * binomial(2*n-6*k+1,2*k).

1, 1, 1, 1, 7, 21, 43, 73, 131, 297, 715, 1593, 3259, 6553, 13723, 29833, 64827, 137881, 289179, 608329, 1293083, 2762457, 5885179, 12478601, 26418363, 56028761, 119072987, 253139017, 537620571, 1140840793, 2420927291, 5139947401, 10916332411, 23182447833

Offset

0,5

Links

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

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^4).

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+1, 2*k], {k, 0, Floor[n/4]}], {n, 0, 40}] (* Vincenzo Librandi, Sep 04 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\4, 2^k*binomial(2*n-6*k+1, 2*k));
(Magma) [&+[2^k* Binomial(2*n-6*k+1, 2*k): k in [0..Floor (n/4)]]: n in [0..35]]; // Vincenzo Librandi, Sep 04 2025

Crossrefs

Cf. A002315, A387624, A387625.

Sequence in context: A054569 A380279 A077354 * A246430 A387625 A256051

Adjacent sequences: A387623 A387624 A387625 * A387627 A387628 A387629

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 03 2025

Status

approved