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A224295 Number of permutations of length n avoiding 12345 and 12354. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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

LINKS

Table of n, a(n) for n=0..25.

Alice L. L. Gao, Sergey Kitaev, On partially ordered patterns of length 4 and 5 in permutations, arXiv:1903.08946 [math.CO], 2019.

Alice L. L. Gao, 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, 2013.

MAPLE

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

CROSSREFS

Cf. A006318.

Sequence in context: A224318 A079106 A247472 * A263777 A088713 A193938

Adjacent sequences:  A224292 A224293 A224294 * A224296 A224297 A224298

KEYWORD

nonn

AUTHOR

Brian Nakamura, Apr 03 2013

EXTENSIONS

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

STATUS

approved

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Last modified June 21 19:12 EDT 2021. Contains 345365 sequences. (Running on oeis4.)