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%I #55 Jun 12 2021 12:27:15
%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 Lim_{n->infinity} a(n)^(1/n) >= 9.4854... (a new rigorous lower bound). Lim_{n->infinity} = 9.69963634535... (conjecture). [Defant, Elvey Price, Guttmann, 2020] - _Vaclav Kotesovec_, Jun 12 2021, following a suggestion of _Anthony Guttmann_
%H Colin Defant, Andrew Elvey Price, and Anthony J. Guttmann, <a href="/A134664/b134664.txt">Table of n, a(n) for n = 1..1000</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 Colin 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.
%H Colin Defant, Andrew Elvey Price, and Anthony J. Guttmann, <a href="https://arxiv.org/abs/2009.10439">Asymptotics of 3-stack-sortable permutations</a>, arXiv:2009.10439 [math.CO], 2020.
%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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