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A329700 Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UH, HH and HD. 1
1, 1, 1, 2, 3, 5, 9, 16, 30, 56, 108, 208, 409, 805, 1606, 3211, 6479, 13108, 26691, 54499, 111808, 229983, 474787, 982528, 2039143, 4241187, 8842137, 18469760, 38657209, 81047625, 170212312, 358013615, 754140328, 1590709427, 3359666293, 7104369046, 15040357081, 31875827699 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

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.

LINKS

Table of n, a(n) for n=0..37.

Andrei Asinowski, Cyril Banderier, and Valerie Roitner, Generating functions for lattice paths with several forbidden patterns, preprint, 2019.

FORMULA

G.f.: (1+t)*(1-t^3-sqrt(1-4t^2-2t^3+t^6))/(2t^2).

EXAMPLE

a(4)=3 since we have 3 excursions of length 4, namely UUDD, UDUD and HUDH.

CROSSREFS

Cf. A329699.

Sequence in context: A050168 A331966 A072176 * A217282 A047061 A136169

Adjacent sequences:  A329697 A329698 A329699 * A329701 A329702 A329703

KEYWORD

nonn,walk

AUTHOR

Valerie Roitner, Dec 16 2019

STATUS

approved

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Last modified April 11 15:49 EDT 2021. Contains 342886 sequences. (Running on oeis4.)