

A324916


Triangle read by rows: T(n,k) is the number of 3stacksortable permutations of [n] with k descents (0 <= k <= n1).


2



1, 1, 1, 1, 4, 1, 1, 11, 11, 1, 1, 25, 62, 25, 1, 1, 50, 252, 252, 50, 1, 1, 91, 833, 1644, 833, 91, 1, 1, 154, 2375, 8183, 8183, 2375, 154, 1, 1, 246, 6045, 33655, 58007, 33655, 6045, 246, 1, 1, 375, 14049, 119737, 327269, 327269, 119737, 14049, 375, 1
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OFFSET

1,5


COMMENTS

Bona has proven that the polynomial Sum_{k=0..n1} T(n,k)*x^k is always symmetric and unimodal. He has conjectured that it has only real roots.


LINKS

Colin Defant, Table of n, a(n) for n = 1..945
M. Bona, Symmetry and unimodality in tstacksortable permutations, J. Combin. Theory Ser. A, 98 (2002), 201209.
M. Bona, A survey of stacksorting disciplines, Electron. J. Combin., 9 (2003), Article #A1.
C. Defant, Counting 3stacksortable permutations, arXiv:1903.09138 [math.CO], 2019.
C. Defant, Preimages under the stacksorting algorithm, arXiv:1511.05681 [math.CO], 20152018; Graphs Combin., 33 (2017), 103122.


FORMULA

See the paper "Counting 3StackSortable Permutations" for a recurrence that generates this sequence.


EXAMPLE

T(5,1)=25 because there are 25 3stacksortable permutations of {1,2,3,4,5} with exactly 1 descent.


CROSSREFS

Row sums give A134664.
Sequence in context: A152970 A154986 A154983 * A156534 A168287 A221987
Adjacent sequences: A324913 A324914 A324915 * A324917 A324918 A324919


KEYWORD

nonn,tabl


AUTHOR

Colin Defant, Mar 18 2019


STATUS

approved



