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A329675
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Number of meanders of length n with Motzkin-steps avoiding the consecutive steps UD and HH.
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1
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1, 2, 3, 6, 12, 24, 50, 105, 221, 471, 1008, 2164, 4669, 10102, 21909, 47642, 103801, 226549, 495284, 1084318, 2376902, 5216543, 11460725, 25203497, 55475172, 122205631, 269408827, 594343482, 1312035579, 2898123874, 6405224773, 14163866716, 31336109418, 69360335726
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OFFSET
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0,2
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COMMENTS
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The Motzkin step set is U=(1,1), H=(1,0) and D=(1,-1). A meander is a path starting at (0,0) 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.: -(1-2*t-t^2+t^3-sqrt(t^6+2*t^5-3*t^4-6*t^3-2*t^2+1))/(2*t*(1-2*t-t^2+t^3)).
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EXAMPLE
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a(3)=6 since we have 6 meanders of length 3, namely UUU, UUH, UHU, UHD, HUU and HUH.
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CROSSREFS
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Cf. A329676 which counts excursions avoiding consecutive UD and HH.
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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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