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%I #26 Feb 05 2024 09:25:27
%S 1,1,2,6,24,118,672,4256,29176,212586,1625704,12930160,106242392,
%T 897210996,7756325952,68422701792,614341492144,5602330498170,
%U 51798365474872,484856381630288,4589003801130456,43870126242653020,423219224419273888,4116816114087389056,40351014094161799568,398270701521760650532
%N Number of permutations of length n avoiding 12345 and 12354.
%C Conjectured to be the number of permutations of length n avoiding the partially ordered pattern (POP) {2>1>5>3, 5>4} of length 5. That is, conjectured to be the number of length n permutations having no subsequences of length 5 in which the elements 3 and 4 are the smallest, and the element in position 2 is larger than that in position 1, which in turn is larger than the element in position 5.- _Sergey Kitaev_, Dec 13 2020
%C Restatement of the comment by Kitaev: Conjectured to be the number of permutations of length n avoiding patterns 45123 and 45213. - _Alexander Burstein_, Feb 05 2024
%H Jay Pantone, <a href="/A224295/b224295.txt">Table of n, a(n) for n = 0..790</a>
%H Michael H. Albert, Christian Bean, Anders Claesson, Émile Nadeau, Jay Pantone, and Henning Ulfarsson, <a href="https://arxiv.org/abs/2202.07715">Combinatorial Exploration: An algorithmic framework for enumeration</a>, arXiv:2202.07715 [math.CO], 2022.
%H Michael H. Albert, Christian Bean, Anders Claesson, Émile Nadeau, Jay Pantone, and Henning Ulfarsson, <a href="https://permpal.com/perms/basis/01234_01243/">PermPAL Database</a>
%H Christian Bean, Émile Nadeau, Jay Pantone, and Henning Ulfarsson, <a href="https://arxiv.org/abs/2312.07716">Permutations avoiding bipartite partially ordered patterns have a regular insertion encoding</a>, arXiv:2312.07716 [math.CO], 2023.
%H Alice L. L. Gao and Sergey Kitaev, <a href="https://arxiv.org/abs/1903.08946">On partially ordered patterns of length 4 and 5 in permutations</a>, arXiv:1903.08946 [math.CO], 2019.
%H Alice L. L. Gao and Sergey Kitaev, <a href="https://doi.org/10.37236/8605">On partially ordered patterns of length 4 and 5 in permutations</a>, The Electronic Journal of Combinatorics 26(3) (2019), P3.26.
%H B. Nakamura, <a href="http://arxiv.org/abs/1301.5080">Approaches for enumerating permutations with a prescribed number of occurrences of patterns</a>, arXiv 1301.5080 [math.CO], 2013.
%p # Programs can be obtained from author's personal website.
%Y Cf. A006318.
%K nonn
%O 0,3
%A _Brian Nakamura_, Apr 03 2013
%E a(0)=1 prepended by _Alois P. Heinz_, Dec 13 2020
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