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A329677
Number of excursions of length n with Motzkin-steps consisting only of consecutive steps UH, HD, and DH.
2
1, 1, 0, 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
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^3 + t^4.
EXAMPLE
We only have the following four excursions of this type: the empty walk, H, UHD and UHDH.
MATHEMATICA
PadRight[#, 105] &@ CoefficientList[Series[1 + x + x^3 + x^4, {x, 0, 105}], x] (* Michael De Vlieger, Dec 16 2019 *)
CROSSREFS
Cf. A329670, A329678, A329679 (other Motzkin excursions avoiding certain consecutive steps such that the sequence counting them has growth rate zero).
Sequence in context: A284793 A260397 A137161 * A077050 A128432 A195198
KEYWORD
nonn,walk,easy
AUTHOR
Valerie Roitner, Dec 16 2019
STATUS
approved