[seqfan] Number of ways to connect sets of k dots in a perfect n-gon

jnthn stdhr jstdhr at gmail.com
Sat Apr 21 19:32:01 CEST 2018


 I noticed this awhile back and assume it will be of interest...

"Let Q(n,k) be the number of ways in which we can connect sets of k
vertices in a given perfect n-gon such that no two lines intersect at the
interior of the n-gon and no vertex remains isolated."

This is from:
https://math.stackexchange.com/questions/1294224/number-of-ways-to-connect-sets-of-k-dots-in-a-perfect-n-gon

It mentions various sequences already in the database, most notably the
catalan numbers, as well as:

1,4,22,210,2244,29026,404064,... ( https://oeis.org/draft/A303330 )
3,9,54,567,4617,62694,813564,11973825,... ( https://oeis.org/draft/A303331 )
8,64,1536,45056,1703936,80478208,...  ( https://oeis.org/draft/A303332 )

Would anyone who is interested please double-check the terms in the three
sequences above, correct their offsets, and add appropriate names?

 Are there other sequences of interest not already calculated?

I would be curious to see what new sequences arise from this, so please
update this post with any new A-numbers, if added.

Cheers,

-Jonathan



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