OFFSET
0,2
COMMENTS
In nondeterministic walks (N-walks) the steps are sets and called N-steps. N-walks start at 0 and are concatenations of such N-steps such that all possible extensions are explored in parallel. The nondeterministic Dyck step set is { {-1}, {1}, {-1,1} }. Such an N-walk is called an N-excursion if it contains at least one trajectory that is a classical excursion, i.e., never crosses the x-axis, and starts and ends at 0 (for more details see the de Panafieu-Wallner article).
LINKS
Élie de Panafieu and Michael Wallner, Combinatorics of nondeterministic walks, arXiv:2311.03234 [math.CO], 2023.
FORMULA
G.f.: (1-8*x-(1-12*x)*sqrt(1-8*x))/(8*x*(1-9*x)).
EXAMPLE
The a(1)=4 N-bridges of length 2 are
/ /
/\, /\, /\, /\
\ \/
\ \
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Wallner, Dec 18 2023
STATUS
approved