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A329668
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Number of meanders of length n with Motzkin-steps avoiding the consecutive steps HH and DU.
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1
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1, 2, 4, 9, 18, 38, 81, 171, 366, 787, 1693, 3661, 7938, 17240, 37540, 81892, 178907, 391483, 857769, 1881618, 4132225, 9083823, 19986954, 44014447, 97002134, 213933655, 472137851, 1042626752, 2303780392, 5093189194, 11265742842, 24930884645, 55196469010, 122255756284
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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+1)*((t^3 - t^2 - 2*t + 1)*(t+1) - (1-t)*sqrt((t^3 - t^2 - 2*t + 1)*(t^3 + 3*t^2 + 2*t + 1)))/((t^3 - t^2 - 2*t + 1)*t^2).
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EXAMPLE
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a(3)=9 as one has 9 meanders of length 3, namely: UUU, UUH, UUD, UDH, UHU, UHD, HUU, HUD and HUH.
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CROSSREFS
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Cf. A329666, which counts excursions with same restrictions.
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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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