A390337 a(n) = Sum_{k=0..n} binomial(3*n+k-1,n-k).

1, 3, 17, 103, 643, 4082, 26193, 169324, 1100561, 7183179, 47037770, 308839996, 2032250927, 13397582173, 88463267588, 584916078291, 3872067079555, 25659566239274, 170200888987121, 1129893804436178, 7506551997419770, 49904474883265592, 331976969392263124

Offset

0,2

Links

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

Formula

G.f.: 1/(g * (1-3*x*g^2) * (1-x*g^4)) where g = 1+x*g^3 is the g.f. of A001764.

a(n) = Sum_{k=0..n} binomial(3*n-1,n-k) * Fibonacci(k+1).

Mathematica

Table[Sum[Binomial[3* 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(3*n+k-1, n-k));
(Magma) [&+[Binomial(3*n+k-1, n-k): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Jan 03 2026

Crossrefs

Cf. A088305, A279014, A390338, A390339.

Cf. A038736, A038744, A390238.

Cf. A000045, A001764.

Sequence in context: A116886 A164816 A163064 * A020069 A020024 A264963

Adjacent sequences: A390334 A390335 A390336 * A390338 A390339 A390340

Keyword

nonn

Author

Seiichi Manyama, Nov 01 2025

Status

approved