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A329694
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Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UU, HH and DU.
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1
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1, 1, 1, 3, 3, 3, 8, 12, 13, 27, 50, 64, 109, 215, 322, 504, 966, 1616, 2526, 4578, 8115, 13143, 22836, 41162, 69410, 118536, 212498, 369226, 631631, 1119755, 1977612, 3419130, 6014450, 10684128, 18689970, 32807722, 58300072, 102905556, 181031164, 321348824, 570303658, 1007402762
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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)*(1-2t^3-sqrt(1-4t^3-4t^4))/(2t^4).
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EXAMPLE
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a(4)=3 since we have the following 3 excursions of length 4: UHDH, HUHD 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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