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A257387
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Number of Motzkin paths of length n with no level steps at height 4.
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1
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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
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OFFSET
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0,3
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..1000
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FORMULA
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A005043, A217312, A252354, A257386.
Sequence in context: A230554 A005207 A257519 * A094286 A094287 A094288
Adjacent sequences: A257384 A257385 A257386 * A257388 A257389 A257390
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KEYWORD
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nonn
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AUTHOR
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José Luis Ramírez Ramírez, Apr 21 2015
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STATUS
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approved
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