A387629 a(n) = Sum_{k=0..floor(n/4)} 2^k * binomial(2*n-6*k+1,2*k+1).

1, 3, 5, 7, 11, 31, 83, 183, 351, 675, 1435, 3231, 7119, 14987, 30963, 64871, 138775, 298403, 636091, 1344191, 2838399, 6021371, 12818467, 27277207, 57911207, 122790675, 260485131, 553185519, 1175285967, 2496108459, 5298760307, 11246985927, 23877452663, 50702334403

Offset

0,2

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 - 4*x).

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+1], {k, 0, Floor[n/3]}], {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+1));
(Magma) [&+[2^k* Binomial(2*n-6*k+1, 2*k+1): k in [0..Floor (n/4)]]: n in [0..35]]; // Vincenzo Librandi, Sep 04 2025

Crossrefs

Cf. A001653, A387627, A387628.

Cf. A387623, A387626.

Sequence in context: A379450 A061245 A361898 * A230139 A242944 A137355

Adjacent sequences: A387626 A387627 A387628 * A387630 A387631 A387632

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 03 2025

Status

approved