A224295 Number of permutations of length n avoiding 12345 and 12354.

1, 1, 2, 6, 24, 118, 672, 4256, 29176, 212586, 1625704, 12930160, 106242392, 897210996, 7756325952, 68422701792, 614341492144, 5602330498170, 51798365474872, 484856381630288, 4589003801130456, 43870126242653020, 423219224419273888, 4116816114087389056, 40351014094161799568, 398270701521760650532

Offset: 0

Author

Brian Nakamura, Apr 03 2013

Keywords

• nonn

Comments

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

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

Links

• Jay Pantone, Table of n, a(n) for n = 0..790
• Michael H. Albert, Christian Bean, Anders Claesson, Émile Nadeau, Jay Pantone, and Henning Ulfarsson, Combinatorial Exploration: An algorithmic framework for enumeration, arXiv:2202.07715 [math.CO], 2022.
• Michael H. Albert, Christian Bean, Anders Claesson, Émile Nadeau, Jay Pantone, and Henning Ulfarsson, PermPAL Database
• Christian Bean, Émile Nadeau, Jay Pantone, and Henning Ulfarsson, Permutations avoiding bipartite partially ordered patterns have a regular insertion encoding, The Electronic Journal of Combinatorics, Volume 31, Issue 3 (2024); arXiv preprint, arXiv:2312.07716 [math.CO], 2023.
• Alice L. L. Gao and Sergey Kitaev, On partially ordered patterns of length 4 and 5 in permutations, arXiv:1903.08946 [math.CO], 2019.
• Alice L. L. Gao and Sergey Kitaev, On partially ordered patterns of length 4 and 5 in permutations, The Electronic Journal of Combinatorics 26(3) (2019), P3.26.
• B. Nakamura, Approaches for enumerating permutations with a prescribed number of occurrences of patterns, arXiv 1301.5080 [math.CO], 2013.

Crossrefs

Cf. A006318.

Programs

Maple

# Programs can be obtained from author's personal website.

Extensions

a(0)=1 prepended by Alois P. Heinz, Dec 13 2020