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A257386
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Number of Motzkin paths of length n with no level steps at height 3.
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2
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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
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OFFSET
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0,3
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LINKS
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FORMULA
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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).
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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+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+x-sqrt(1-2*x-3*x^2))/(2*x*(1+x)))))))) \\ G. C. Greubel, Apr 08 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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