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A257516
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Number of 3-generalized Motzkin paths of length n with no level steps H=(3,0) at even level.
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1
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1, 0, 1, 0, 2, 1, 5, 4, 15, 15, 48, 57, 162, 218, 570, 842, 2070, 3284, 7709, 12922, 29299, 51255, 113220, 204781, 443574, 823554, 1757947, 3331818, 7035054, 13552699, 28387680, 55401396, 115369417, 227501256, 471780468, 938107057, 1939727280, 3883120002
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OFFSET
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0,5
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LINKS
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FORMULA
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G.f.: (1-x^3-sqrt((1-x^3)*(1-4*x^2-x^3)))/(2*x^2).
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EXAMPLE
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For n=6 we have 5 paths: UDUDUD, UUDDUD, UDUUDD, UUUDDD and UUDUDD
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MATHEMATICA
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CoefficientList[Series[(1-x^3-Sqrt[(1-x^3)*(1-4*x^2-x^3)])/(2*x^2), {x, 0, 20}], x] (* Vaclav Kotesovec, Apr 27 2015 *)
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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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