A387551 a(n) = (1/2) * Sum_{k=0..floor(n/2)} 2^k * binomial(2*k+2,2*n-4*k+1).

1, 0, 4, 4, 12, 40, 44, 224, 304, 992, 2208, 4480, 13200, 24320, 68608, 145856, 345920, 848256, 1834432, 4644864, 10239488, 24708096, 57602048, 132493312, 318103808, 724885504, 1728687104, 4003968000, 9371413504, 22045935616, 51113446400, 120583479296

Offset: 0

Author

Seiichi Manyama, Sep 01 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 (0,4,4,-4,8,-4).

Crossrefs

Cf. A387476.

Programs

Magma

[&+[2^k * Binomial(2*k+2, 2*n-4*k+1)/2: k in [0..Floor(n/2)]]: n in [0..40]]; // Vincenzo Librandi, Sep 02 2025

Mathematica

Table[Sum[2^k*Binomial[2*k+2, 2*n-4*k+1]/2,{k,0,Floor[n/2]}],{n,0,40}] (* Vincenzo Librandi, Sep 02 2025 *)

PARI

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

Formula

G.f.: B(x)^2, where B(x) is the g.f. of A387476.

G.f.: 1/((1-2*x^2-2*x^3)^2 - 16*x^5).

a(n) = 4*a(n-2) + 4*a(n-3) - 4*a(n-4) + 8*a(n-5) - 4*a(n-6).