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A319031 Triangle read by rows: T(n,k) is the number of permutations pi of [k] such that s(pi) avoids the pattern 12...n, where s is West's stack-sorting map (1 <= k <= 2^(n-1)-1). 0
1, 1, 2, 1, 1, 2, 6, 10, 13, 10, 3, 1, 2, 6, 24, 78, 232, 631, 1498, 3017, 4934 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,3
COMMENTS
We only consider k <= 2^(n-1)-1 because T(n,k) = 0 when k >= 2^(n-1).
It appears that the rows T(n,1), ..., T(n,2^(n-1)-1) are unimodal.
LINKS
Colin Defant, Stack-sorting preimages of permutation classes, arXiv:1809.03123 [math.CO], 2018.
EXAMPLE
The only permutation pi of [3] such that s(pi) does not contain the pattern 123 is 231, so T(3,3) = 1.
Triangle begins:
1,
1, 2, 1,
1, 2, 6, 10, 13, 10, 3,
1, 2, 6, 24, 78, 232, 631, 1498, 3017, 4934, ...
(not all terms in the fourth row are known).
CROSSREFS
Sequence in context: A007736 A107042 A134830 * A022874 A022873 A323739
KEYWORD
nonn,tabf,more
AUTHOR
Colin Defant, Sep 10 2018
STATUS
approved

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Last modified June 20 10:31 EDT 2024. Contains 373516 sequences. (Running on oeis4.)