A387552 a(n) = (1/2) * Sum_{k=0..floor(n/3)} 2^k * binomial(2*k+2,2*n-6*k+1).

1, 0, 0, 4, 4, 0, 12, 40, 12, 32, 224, 224, 112, 960, 2016, 1152, 3600, 12672, 13120, 15168, 64256, 110848, 99904, 291200, 734912, 836608, 1376256, 4114432, 6516224, 8042496, 20953088, 43890688, 56483072, 107188224, 260720640, 404997120, 609147904, 1431527424

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 (0,0,4,4,0,-4,8,-4).

Crossrefs

Cf. A387477.

Programs

Magma

[&+[2^k * Binomial(2*k+2, 2*n-6*k+1)/2: k in [0..Floor(n/3)]]: n in [0..40]]; // Vincenzo Librandi, Sep 02 2025

Mathematica

Table[Sum[2^k*Binomial[2*k+2, 2*n-6*k+1]/2,{k,0,Floor[n/3]}],{n,0,40}] (Vincenzo Librandi, Sep 02 2025 *)

PARI

a(n) = sum(k=0, n\3, 2^k*binomial(2*k+2, 2*n-6*k+1))/2;

Formula

G.f.: B(x)^2, where B(x) is the g.f. of A387477.

G.f.: 1/((1-2*x^3-2*x^4)^2 - 16*x^7).

a(n) = 4*a(n-3) + 4*a(n-4) - 4*a(n-6) + 8*a(n-7) - 4*a(n-8).