A389361 a(n) = Sum_{k=0..n} binomial(4*n+k,n-k).

1, 5, 38, 313, 2673, 23307, 206009, 1838554, 16527302, 149405885, 1356719781, 12365705324, 113055426671, 1036348332062, 9521448727351, 87650805491723, 808277849339849, 7465032302793027, 69039459131717570, 639289082518689361, 5926248581784399853

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..900

Formula

G.f.: 1/((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,n-k) * Fibonacci(k+1).

a(n) ~ 2^(8*n + 1/2) / (5 * sqrt(Pi*n) * 3^(3*n - 3/2)). - Vaclav Kotesovec, Nov 05 2025

Mathematica

Table[Sum[Binomial[4*n+k, n-k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Nov 05 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(4*n+k, n-k));
(Magma) [&+[Binomial(4*n+k, n-k): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 12 2025

Crossrefs

Cf. A038736, A108080, A122367.

Cf. A390333, A390335, A390338.

Cf. A000045, A002293.

Sequence in context: A073508 A282964 A391466 * A357163 A357224 A384824

Adjacent sequences: A389358 A389359 A389360 * A389362 A389363 A389364

Keyword

nonn

Author

Seiichi Manyama, Nov 01 2025

Status

approved