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A263867
Number of non-overlapping permutations of length n. A permutation is non-overlapping (sometimes called minimally overlapping) if the shortest permutation containing two occurrences of it as a consecutive pattern has length 2n-1.
2
2, 4, 12, 48, 280, 1864, 14840, 132276, 1323504
OFFSET
2,1
LINKS
Miklós Bóna, Non-overlapping permutation patterns, PU. M. A. 22(2):99-105, 2011.
Sergi Elizalde and Peter R. W. McNamara, The structure of the consecutive pattern poset, arXiv:1508.05963 [math.CO], 2015. See p. 21.
Sergey Kirgizov and Khaydar Nurligareev, Asymptotics of self-overlapping permutations, arXiv:2311.11677 [math.CO], 2023. See p. 2.
FORMULA
For n>=3, a(n) is divisible by 4 (shown in the Elizalde/McNamara link).
The limit of a(n)/n! is approximately 0.364 (shown by M. Bóna).
An implicit formula of a(n) is given in Section 3 of Pan and Remmel's paper.
EXAMPLE
There are 4 non-overlapping permutations of length 3, namely 132, 213, 231 and 312.
CROSSREFS
Sequence in context: A030949 A030888 A030801 * A326863 A372145 A082480
KEYWORD
nonn,more
AUTHOR
Sergi Elizalde, Oct 28 2015
STATUS
approved