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A329683
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Number of excursions of length n with Motzkin-steps forbidding all consecutive steps of length 2 except UH, HH and HD.
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3
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1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2
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OFFSET
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0,4
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COMMENTS
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The Motzkin step set is U=(1,1), H=(1,0) and D=(1,-1). An excursion is a path starting at (0,0), ending on the x-axis and never crossing the x-axis, i.e., staying at nonnegative altitude.
This sequence is periodic with a pre-period of length 3 (namely 1, 1, 1) and a period of length 1 (namely 2).
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LINKS
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FORMULA
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G.f.: (1 + t^3)/(1 - t).
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EXAMPLE
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For n >= 3 we always have two allowed excursions, namely UH^(n-2)D and H^n.
For n = 0, 1, 2 we have one meander each, namely the empty walk, H and HH.
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CROSSREFS
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KEYWORD
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nonn,walk,easy
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AUTHOR
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STATUS
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approved
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