A390338 a(n) = Sum_{k=0..n} binomial(4*n+k-1,n-k).

1, 4, 30, 245, 2080, 18058, 159081, 1415955, 12700610, 114602665, 1039058616, 9457679477, 86366895485, 790883332085, 7259563932465, 66773806050440, 615303031588120, 5678955971238490, 52489049602086585, 485764513113096465, 4500754571267198440

Offset

0,2

Links

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

Formula

G.f.: 1/(g * (1-4*x*g^3) * (1-x*g^5)) where g = 1+x*g^4 is the g.f. of A002293.

a(n) = Sum_{k=0..n} binomial(4*n-1,n-k) * Fibonacci(k+1).

Mathematica

Table[Sum[Binomial[4* n+k-1, n-k], {k, 0, n}], {n, 0, 28}] (* Vincenzo Librandi, Jan 03 2026 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(4*n+k-1, n-k));
(Magma) [&+[Binomial(4*n+k-1, n-k): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Jan 03 2026

Crossrefs

Cf. A088305, A279014, A390337, A390339.

Cf. A389361, A390333, A390335.

Cf. A000045, A002293.

Sequence in context: A052604 A391492 A388530 * A357204 A038225 A086452

Adjacent sequences: A390335 A390336 A390337 * A390339 A390340 A390341

Keyword

nonn

Author

Seiichi Manyama, Nov 01 2025

Status

approved