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A307786 Number of valid hook configurations of 312-avoiding permutations of [n]. 1
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 (list; graph; refs; listen; history; text; internal format)



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.


Table of n, a(n) for n=0..25.

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.


Appears to be the binomial transform of A151347.

Sequence in context: A148335 A268419 A149883 * A149884 A149885 A149886

Adjacent sequences:  A307783 A307784 A307785 * A307787 A307788 A307789




Colin Defant, Apr 28 2019



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Last modified July 2 09:32 EDT 2022. Contains 354999 sequences. (Running on oeis4.)