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A329691
Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UD, HU, HH and DH.
3
1, 1, 0, 1, 0, 1, 1, 1, 3, 2, 6, 7, 11, 21, 25, 52, 71, 121, 204, 302, 547, 828, 1417, 2333, 3752, 6454, 10344, 17592, 29097, 48292, 81756, 134961, 228740, 381917, 642048, 1084489, 1817732, 3080591, 5185373, 8772149, 14850172, 25098840, 42612096, 72156764, 122552908, 208140274
OFFSET
0,9
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.
FORMULA
G.f.: (1+t^2+t^3-sqrt(1-2t^2-2t^3+t^4-2t^5+t^6))/(2t^2).
EXAMPLE
a(8)=3 since we have the following 3 excursions of length 8: UUHDDUHD, UHDUUHDD and UUHDUHDD.
CROSSREFS
Sequence in context: A230267 A286226 A269852 * A293204 A273344 A370665
KEYWORD
nonn,walk
AUTHOR
Valerie Roitner, Dec 06 2019
STATUS
approved