A387767 a(n) = Sum_{k=0..n} 2^k * binomial(2*k+1,2*n-2*k+1).

1, 6, 22, 96, 428, 1864, 8136, 35584, 155536, 679776, 2971232, 12986880, 56763584, 248105088, 1084430464, 4739883008, 20717318400, 90552296960, 395790530048, 1729941135360, 7561313643520, 33049369626624, 144453845469184, 631386126483456, 2759694208372736

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,0,8,-4).

Formula

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

a(n) = 4*a(n-1) + 8*a(n-3) - 4*a(n-4).

Mathematica

CoefficientList[Series[(1+2*x-2*x^2)/((1+2*x-2*x^2)^2 - 8*x), {x, 0, 24}], x] (* Stefano Spezia, Sep 08 2025 *)
Table[Sum[2^k*Binomial[2*k+1, 2*n-2*k+1], {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Sep 12 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, 2^k*binomial(2*k+1, 2*n-2*k+1));
(Magma) [&+[2^k * Binomial(2*k+1, 2*n-2*k+1): k in [0..n]]: n in [0..25]]; // Vincenzo Librandi, Sep 12 2025

Crossrefs

Cf. A387768, A387769.

Cf. A108485, A387764.

Sequence in context: A349834 A379436 A240049 * A078418 A100300 A027296

Adjacent sequences: A387764 A387765 A387766 * A387768 A387769 A387770

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 07 2025

Status

approved