|
|
A368164
|
|
Number of nondeterministic Dyck bridges of length 2*n.
|
|
2
|
|
|
1, 7, 63, 583, 5407, 50007, 460815, 4231815, 38745279, 353832631, 3224323183, 29328492519, 266364307231, 2416023142423, 21890268365007, 198151683934023, 1792260214473087, 16199857938091383, 146342491104098607, 1321339563995562663, 11925412051760977887, 107590261672922633943
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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-bridge if it contains at least one trajectory that is a classical bridge, i.e., starts and ends at 0 (for more details see the de Panafieu-Wallner article).
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (1-6*t)/(sqrt(1-8*t)*(1-9*t)).
|
|
EXAMPLE
|
The a(1)=7 N-bridges of length 2 are
/ / /
/\, , /\, , /\, / , /\
\/ \/ \ \/ \/
\ \ \
|
|
CROSSREFS
|
Cf. A151281 (nondeterministic Dyck meanders), A368234 (nondeterministic Dyck excursions), A000244 (nondeterministic Dyck walks).
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|