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A257386 Number of Motzkin paths of length n with no level steps at height 3. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 10 01:30 EDT 2021. Contains 343747 sequences. (Running on oeis4.)