A387846 a(n) = Sum_{k=0..n} binomial(3*n,4*k).

1, 1, 16, 136, 992, 8256, 65536, 523776, 4196352, 33550336, 268435456, 2147516416, 17179738112, 137439215616, 1099511627776, 8796090925056, 70368752566272, 562949936644096, 4503599627370496, 36028797153181696, 288230375614840832, 2305843010287435776

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..700

Index entries for linear recurrences with constant coefficients, signature (4,24,64).

Formula

G.f.: (1-3*x-12*x^2-16*x^3)/((1-8*x) * (1+4*x+8*x^2)).

a(n) = 4*a(n-1) + 24*a(n-2) + 64*a(n-3) for n > 3.

For n > 0, a(n) = 2^(3*n-2) + 2^(3*n/2-1)*cos(3*Pi*n/4). - Vaclav Kotesovec, Oct 16 2025

Mathematica

Table[Sum[Binomial[3*n, 4*k], {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Sep 15 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(3*n, 4*k));
(Magma) [&+[Binomial(3*n, 4*k): k in [0..n]]: n in [0..25]]; // Vincenzo Librandi, Sep 15 2025

Crossrefs

Cf. A070775.

Sequence in context: A341227 A022581 A383913 * A278283 A329370 A351698

Adjacent sequences: A387843 A387844 A387845 * A387847 A387848 A387849

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 10 2025

Status

approved