OFFSET
0,3
COMMENTS
The class of a Motzkin path is the set of indices i such that the i-th non-down step is an east step. For n > 0, a(n) is the number of pairs (P,Q) of Motzkin paths such that P and Q have the same class and P lies below or is equal to Q.
Conjecture: This sequence is the binomial transform of A151347.
The Defant article gives a functional equation that defines a generating function Q(x,y,z) such that Q(x,0,0) is the ordinary generating function of this sequence.
LINKS
Colin Defant, Motzkin intervals and valid hook configurations, arXiv preprint arXiv:1904.10451 [math.CO], 2019.
Wenjie Fang, A partial order on Motzkin paths, arXiv preprint arXiv:1801.04809 [math.CO], 2018.
CROSSREFS
KEYWORD
nonn
AUTHOR
Colin Defant, Apr 28 2019
STATUS
approved