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A329678
Number of excursions of length n with Motzkin-steps consisting only of consecutive steps UD and DH.
3
1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
OFFSET
0
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 on the x-axis and never crossing the x-axis, i.e., staying at nonnegative altitude.
FORMULA
G.f.: 1 + t + t^2 + t^3.
EXAMPLE
We only have the following four excursions of this type: the empty walk, H, UD and UDH.
CROSSREFS
Cf. A329670, A329677, A329679 (other Motzkin excursions avoiding certain consecutive steps such that the sequence counting them has growth rate zero).
Sequence in context: A293163 A359832 A267871 * A359942 A266434 A025447
KEYWORD
nonn,walk,easy
AUTHOR
Valerie Roitner, Dec 16 2019
STATUS
approved