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A134664 Number of 3-stack sortable permutations on n letters. 3

%I

%S 1,2,6,24,114,606,3494,21426,137901,922862,6377818,45281958,328969075,

%T 2437728712,18378435667,140675908516,1091364628837,8569030580864,

%U 68010267723813,545061073269660,4407108705811905,35922134951424486,294968178121716449

%N Number of 3-stack sortable permutations on n letters.

%C It is known that 8.65970 < lim_{n--> infinity} a(n)^{1/n} < 12.53296. - _Colin Defant_, Sep 15 2018

%C Conjecture: 9.702 < lim_{n--> infinity} a(n)^{1/n} < 9.704. - _Colin Defant_, Mar 18 2019

%H Colin Defant, <a href="/A134664/b134664.txt">Table of n, a(n) for n = 1..173</a>

%H M. Bona, <a href="https://arxiv.org/abs/1903.04113">Stack words and a bound for 3-stack sortable permutations</a>, arXiv:1903.04113 [math.CO], 2019.

%H M. Bona, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v9i2a1">A survey of stack-sorting disciplines</a>, Electron. J. Combin., 9 (2003), Article #A1.

%H C. Defant, <a href="https://arxiv.org/abs/1903.09138">Counting 3-stack-sortable permutations</a>, arXiv:1903.09138 [math.CO], 2019.

%H C. Defant, <a href="https://arxiv.org/abs/1511.05681">Preimages under the stack-sorting algorithm</a>, arXiv:1511.05681 [math.CO], 2015-2018; Graphs Combin., 33 (2017), 103-122.

%H Colin Defant, <a href="https://arxiv.org/abs/1903.09138">Counting 3-Stack-Sortable Permutations</a>, arXiv:1903.09138 [math.CO], 2019.

%F See the paper "Counting 3-Stack-Sortable Permutations" for a recurrence that generates this sequence. - _Colin Defant_, Mar 18 2019

%e a(5) = 114 because all but the 6 permutations 23451, 24351, 32451, 34251, 42351, 43251 on 5 letters become 12345 after at most 3 passes through the stack sorter.

%Y Cf. A000139, A324917, A324918. Rows sums of A324916.

%K nonn

%O 1,2

%A _Eric Rowland_, Jan 25 2008

%E More terms from _Colin Defant_, Mar 18 2019

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Last modified November 15 08:37 EST 2019. Contains 329144 sequences. (Running on oeis4.)