A367046 G.f. satisfies A(x) = 1 - x^3 + x*A(x)^3.

1, 1, 3, 11, 52, 258, 1344, 7260, 40290, 228363, 1316414, 7694154, 45491247, 271594897, 1635068538, 9914851401, 60503259435, 371269891422, 2289545742174, 14181772631025, 88194284530464, 550444913949048, 3446737067467311, 21647081264988312

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Formula

a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(2*(n-3*k)+1,k) * binomial(3*(n-3*k),n-3*k)/(2*(n-3*k)+1).

Prog

(PARI) a(n) = sum(k=0, n\3, (-1)^k*binomial(2*(n-3*k)+1, k)*binomial(3*(n-3*k), n-3*k)/(2*(n-3*k)+1));

Crossrefs

Cf. A226022, A367047.

Cf. A366676.

Sequence in context: A319155 A362468 A292927 * A179322 A014510 A351067

Adjacent sequences: A367043 A367044 A367045 * A367047 A367048 A367049

Keyword

nonn

Author

Seiichi Manyama, Nov 03 2023

Status

approved