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A329667
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Number of meanders of length n with Motzkin-steps avoiding the consecutive steps UU and HH.
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2
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1, 2, 3, 6, 11, 21, 42, 83, 167, 341, 697, 1437, 2983, 6211, 12996, 27304, 57528, 121601, 257759, 547652, 1166299, 2489010, 5321780, 11398972, 24456235, 52549847, 113077188, 243645011, 525630690, 1135309380, 2454863253, 5313639848, 11512892983, 24967852309
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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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Table of n, a(n) for n=0..33.
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FORMULA
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G.f.: (1/2)*(1-t^3-3*t^2-sqrt(t^6+2*t^5-3*t^4-6*t^3-2*t^2+1))*(t+1)/((t^2+2*t-1)*t^2).
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EXAMPLE
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a(3)=6 since we have 6 meanders of length 3, namely UHU, UDU, UHD, UDH, HUH and HUD.
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PROG
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(PARI) my(t='t+O('t^40)); Vec((1/2)*(1-t^3-3*t^2-sqrt(t^6+2*t^5-3*t^4-6*t^3-2*t^2+1))*(t+1)/((t^2+2*t-1)*t^2)) \\ Michel Marcus, Nov 25 2019
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CROSSREFS
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Cf. A329666 (excursions with same forbidden consecutive steps).
Sequence in context: A008930 A339151 A164362 * A026742 A316471 A018268
Adjacent sequences: A329664 A329665 A329666 * A329668 A329669 A329670
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KEYWORD
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nonn,walk
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AUTHOR
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Valerie Roitner, Nov 25 2019
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STATUS
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approved
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