A307786 Number of valid hook configurations of 312-avoiding permutations of [n].

1, 1, 2, 5, 14, 44, 148, 528, 1972, 7647, 30605, 125801, 529131, 2270481, 9914870, 43973755, 197744417, 900327160, 4145285618, 19280282194, 90507546094, 428476211848, 2044274855774, 9823314566417, 47516954475991, 231260870664189

Offset: 0

Author

Colin Defant, Apr 28 2019

Keywords

• nonn

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

Appears to be the binomial transform of A151347.