A387764 a(n) = Sum_{k=0..n} 2^k * binomial(2*k+1,2*n-2*k).

1, 2, 10, 48, 204, 888, 3896, 17024, 74384, 325152, 1421216, 6211840, 27151040, 118673280, 518702976, 2267172864, 9909473536, 43312824832, 189313870336, 827462578176, 3616715017216, 15808119732224, 69094924072960, 302003566116864, 1320012362256384

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^2).

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

Mathematica

Table[Sum[2^k*Binomial[2*k+1, 2*n-2*k], {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));
(Magma) [&+[2^k * Binomial(2*k+1, 2*n-2*k): k in [0..n]]: n in [0..25]]; // Vincenzo Librandi, Sep 12 2025

Crossrefs

Cf. A387765, A387766.

Cf. A108485, A387767.

Sequence in context: A116194 A054138 A192696 * A181296 A239073 A065982

Adjacent sequences: A387761 A387762 A387763 * A387765 A387766 A387767

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 07 2025

Status

approved