OFFSET
1,2
COMMENTS
It is known that 8.65970 < lim_{n--> infinity} a(n)^{1/n} < 12.53296. - Colin Defant, Sep 15 2018
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
LINKS
Colin Defant, Andrew Elvey Price, and Anthony J. Guttmann, Table of n, a(n) for n = 1..1000
M. Bona, Stack words and a bound for 3-stack sortable permutations, arXiv:1903.04113 [math.CO], 2019.
M. Bona, A survey of stack-sorting disciplines, Electron. J. Combin., 9 (2003), Article #A1.
Colin Defant, Preimages under the stack-sorting algorithm, arXiv:1511.05681 [math.CO], 2015-2018; Graphs Combin., 33 (2017), 103-122.
Colin Defant, Counting 3-Stack-Sortable Permutations, arXiv:1903.09138 [math.CO], 2019.
Colin Defant, Andrew Elvey Price, and Anthony J. Guttmann, Asymptotics of 3-stack-sortable permutations, arXiv:2009.10439 [math.CO], 2020.
FORMULA
See the paper "Counting 3-Stack-Sortable Permutations" for a recurrence that generates this sequence. - Colin Defant, Mar 18 2019
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric Rowland, Jan 25 2008
EXTENSIONS
More terms from Colin Defant, Mar 18 2019
STATUS
approved