A387601 a(n) = (1/2) * Sum_{k=0..floor(n/4)} 2^k * binomial(2*n-6*k+2,2*k+1).

1, 2, 3, 4, 9, 26, 63, 128, 241, 486, 1075, 2412, 5189, 10770, 22343, 47352, 101801, 218142, 462635, 976260, 2065741, 4391914, 9351823, 19877904, 42164785, 89409718, 189779059, 403162268, 856453269, 1818474626, 3859843799, 8193466664, 17396892537, 36942391118

Offset: 0

Author

Seiichi Manyama, Sep 02 2025

Keywords

• nonn
• easy
• new

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).

Crossrefs

Cf. A387508.

Programs

Magma

[&+[2^k* Binomial(2*n-6*k+2, 2*k+1)/2: k in [0..Floor (n/4)]]: n in [0..35]]; // Vincenzo Librandi, Sep 03 2025

Mathematica

Table[Sum[2^k*Binomial[2*n-6*k+2, 2*k+1]/2,{k,0,Floor[n/4]}],{n,0,40}] (* Vincenzo Librandi, Sep 03 2025 *)

PARI

a(n) = sum(k=0, n\4, 2^k*binomial(2*n-6*k+2, 2*k+1))/2;

Formula

G.f.: B(x)^2, where B(x) is the g.f. of A387508.

G.f.: 1/((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).