A257387 Number of Motzkin paths of length n with no level steps at height 4.

1, 1, 2, 4, 9, 21, 51, 127, 323, 834, 2179, 5743, 15238, 40637, 108800, 292200, 786703, 2122387, 5735596, 15522682, 42064028, 114117541, 309918698, 842489130, 2292332265, 6242655886

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} A257386(j)*a(n-j).

G.f: 1/(1-x-x^2*(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+1/2)/(24*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/(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/(1-x-x^2*(1+x-sqrt(1-2*x-3*x^2))/(2*x*(1+x)))))))))) \\ G. C. Greubel, Jun 03 2017

Crossrefs

Cf. A005043, A217312, A252354, A257386.

Sequence in context: A230554 A005207 A257519 * A094286 A094287 A094288

Adjacent sequences: A257384 A257385 A257386 * A257388 A257389 A257390

Keyword

nonn

Author

José Luis Ramírez Ramírez, Apr 21 2015

Status

approved