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A329669
Number of meanders of length n with Motzkin-steps avoiding the consecutive steps HH and DD.
1
1, 2, 4, 10, 23, 54, 129, 307, 733, 1757, 4213, 10115, 24315, 58481, 140741, 338890, 816304, 1966929, 4740758, 11428851, 27557585, 66458601, 160295262, 386671056, 932839439, 2250660384, 5430575647, 13104191607, 31622724351, 76314992880, 184178642468, 444513674334, 1072865869705
OFFSET
0,2
COMMENTS
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.
FORMULA
G.f.: (1/2)*(-t^3 - 3*t^2 - sqrt(t^6 + 2*t^5 - 3*t^4 - 6*t^3 - 2*t^2 + 1) - 2*t + 1)/((t^3 + 3*t^2 + t - 1)*t).
EXAMPLE
a(2)=4 since we have 4 meanders of length two avoiding HH and DD, namely UU, UH, UD and HU.
CROSSREFS
See also A329666, which counts excursions with same restrictions.
Cf. A329667, A329665 (meanders avoiding other sets of step sequences of length 2).
Sequence in context: A094987 A189601 A210460 * A191693 A238436 A366229
KEYWORD
nonn,walk
AUTHOR
Valerie Roitner, Nov 25 2019
STATUS
approved