A257386 Number of Motzkin paths of length n with no level steps at height 3.

1, 1, 2, 4, 9, 21, 51, 126, 316, 799, 2034, 5202, 13357, 34407, 88888, 230237, 597829, 1555962, 4058944, 10612102, 27807135, 73025751, 192204957, 507025163, 1340545113, 3552492126

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

a(n) = a(n-1) + Sum_{j=0..n-2} A252354(j)*a(n-j).

G.f: 1/(1-x-x^2*(1/(1-x-x^2*(1/(1-x-x^2*R(x)))))), where R(x) is the g.f. of Riordan numbers (A005043).

a(n) ~ 3^(n+3/2)/(50*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Apr 24 2015

Mathematica

CoefficientList[Series[1/(1-x-x^2*(1/(1-x-x^2*(1/(1-x-x^2*(1+x-Sqrt[1-2*x-3*x^2])/(2*x*(1+x))))))), {x, 0, 20}], x] (* Vaclav Kotesovec, Apr 24 2015 *)

Prog

(PARI) x='x+O('x^50); Vec(1/(1-x-x^2*(1/(1-x-x^2*(1/(1-x-x^2*(1+x-sqrt(1-2*x-3*x^2))/(2*x*(1+x)))))))) \\ G. C. Greubel, Apr 08 2017

Crossrefs

Cf. A005043, A217312, A252354.

Sequence in context: A091600 A261232 A176334 * A048285 A051529 A230554

Adjacent sequences: A257383 A257384 A257385 * A257387 A257388 A257389

Keyword

nonn

Author

José Luis Ramírez Ramírez, Apr 21 2015

Status

approved