A389471 a(n) = Sum_{k=0..n} binomial(4*k+2,k).

1, 7, 52, 416, 3476, 29810, 260040, 2295840, 20452044, 183463684, 1654906657, 14995689853, 136395340953, 1244571443133, 11387512179033, 104440262098953, 959860898862789, 8837793459924429, 81505374276054865, 752767932923936065, 6961538376227283985

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

G.f.: g^2/((1-4*x*g^3) * (1-x)) where g = 1+x*g^4 is the g.f. of A002293.

Mathematica

Table[Sum[Binomial[ 4*k+2, k], {k, 0, n}], {n, 0, 28}] (* Vincenzo Librandi, Jan 04 2026 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(4*k+2, k));
(Magma) [&+[Binomial(4*k+2, k): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Jan 04 2026

Crossrefs

Partial sums of A257633.

Cf. A224274, A387009, A390335, A390471, A390472, A390473, A390474.

Cf. A002293, A390411.

Sequence in context: A329012 A349532 A369147 * A382917 A162233 A185623

Adjacent sequences: A389468 A389469 A389470 * A389472 A389473 A389474

Keyword

nonn

Author

Seiichi Manyama, Nov 06 2025

Status

approved