A387553 a(n) = (1/2) * Sum_{k=0..floor(n/2)} 2^(n-k) * binomial(2*k+2,2*n-4*k+1).

1, 0, 4, 8, 12, 80, 80, 448, 976, 2176, 8256, 14720, 52416, 124672, 313600, 956416, 2145536, 6438912, 16135168, 42117120, 117754880, 290820096, 812109824, 2091991040, 5519691776, 14911766528, 38335299584, 103777271808, 271034662912, 716987629568, 1911288823808

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 (0,4,8,-4,16,-16).

Crossrefs

Cf. A387483.

Programs

Magma

[&+[2^(n-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^(n-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^(n-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 A387483.

G.f.: 1/((1-2*x^2-4*x^3)^2 - 32*x^5).

a(n) = 4*a(n-2) + 8*a(n-3) - 4*a(n-4) + 16*a(n-5) - 16*a(n-6).