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A329700
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Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UH, HH and HD.
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1
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1, 1, 1, 2, 3, 5, 9, 16, 30, 56, 108, 208, 409, 805, 1606, 3211, 6479, 13108, 26691, 54499, 111808, 229983, 474787, 982528, 2039143, 4241187, 8842137, 18469760, 38657209, 81047625, 170212312, 358013615, 754140328, 1590709427, 3359666293, 7104369046, 15040357081, 31875827699
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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 at (n,0) and never crossing the x-axis, i.e., staying at nonnegative altitude.
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LINKS
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FORMULA
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G.f.: (1+t)*(1-t^3-sqrt(1-4t^2-2t^3+t^6))/(2t^2).
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EXAMPLE
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a(4)=3 since we have 3 excursions of length 4, namely UUDD, UDUD and HUDH.
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CROSSREFS
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KEYWORD
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nonn,walk
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AUTHOR
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STATUS
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approved
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