A234270 G.f.: (1-x)*(1-x-2*x^2-sqrt(1-2*x-3*x^2))/(2*x*(1-2*x-x^2)).

0, 0, 1, 3, 9, 26, 73, 202, 553, 1504, 4073, 11003, 29689, 80094, 216201, 584295, 1581729, 4290648, 11666337, 31802925, 86935089, 238325838, 655282305, 1807106112, 4998491721, 13867056936, 38583280297, 107660033505, 301241301633, 845158142178, 2377277092609

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

J.-L. Baril, J.-M. Pallo, Motzkin subposet and Motzkin geodesics in Tamari lattices, 2013.

Formula

a(n) ~ 3^(n+3/2) / (2*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Apr 28 2014

D-finite with recurrence: (n-3)*(n+1)*a(n) = n*(4*n-11)*a(n-1) - 3*(n-1)*a(n-2) - (n-2)*(8*n-21)*a(n-3) - 3*(n-3)*(n-2)*a(n-4). - Vaclav Kotesovec, Apr 28 2014

Mathematica

CoefficientList[Series[(1 - x) (1 - x-2 x^2 - Sqrt[1 - 2 x - 3 x^2])/(2 x (1 - 2 x - x^2)), {x, 0, 40}], x] (* Vincenzo Librandi, Apr 28 2014 *)

Crossrefs

Cf. A234269.

Sequence in context: A121190 A054447 A061667 * A258911 A268093 A127911

Adjacent sequences: A234267 A234268 A234269 * A234271 A234272 A234273

Keyword

nonn

Author

N. J. A. Sloane, Dec 24 2013

Extensions

Offset changed (from 1 to 0) and more terms added by Vincenzo Librandi, Apr 28 2014

Status

approved