A387600 a(n) = (1/2) * Sum_{k=0..floor(n/3)} 2^k * binomial(2*n-4*k+2,2*k+1).

1, 2, 3, 8, 25, 62, 139, 340, 877, 2186, 5311, 13056, 32497, 80566, 198595, 490092, 1212597, 2999522, 7411207, 18311384, 45265657, 111902478, 276579275, 683566148, 1689580733, 4176276794, 10322491919, 25513684656, 63061990401, 155871106406, 385266605779

Offset: 0

Author

Seiichi Manyama, Sep 02 2025

Keywords

• nonn
• easy
• new

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1500
• Index entries for linear recurrences with constant coefficients, signature (2,-1,4,4,0,-4).

Crossrefs

Cf. A387507.

Programs

Magma

[&+[2^k* Binomial(2*n-4*k+2, 2*k+1)/2: k in [0..Floor (n/3)]]: n in [0..35]]; // Vincenzo Librandi, Sep 03 2025

Mathematica

Table[Sum[2^k*Binomial[2*n-4*k+2, 2*k+1]/2,{k,0,Floor[n/3]}],{n,0,40}] (* Vincenzo Librandi, Sep 03 2025 *)

PARI

a(n) = sum(k=0, n\3, 2^k*binomial(2*n-4*k+2, 2*k+1))/2;

Formula

G.f.: B(x)^2, where B(x) is the g.f. of A387507.

G.f.: 1/((1-x-2*x^3)^2 - 8*x^4).

a(n) = 2*a(n-1) - a(n-2) + 4*a(n-3) + 4*a(n-4) - 4*a(n-6).