login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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)
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

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.

CROSSREFS

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

KEYWORD

nonn

AUTHOR

Colin Defant, Apr 28 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 9 19:51 EST 2019. Contains 329879 sequences. (Running on oeis4.)