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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

LINKS

Table of n, a(n) for n=2..10.

Miklós Bóna, Non-overlapping permutation patterns, PU. M. A. 22(2):99-105, 2011.

Sergi Elizalde, Peter R. W. McNamara, The structure of the consecutive pattern poset, arXiv:1508.05963 [math.CO], 2015.

Ran Pan, Jeffrey B. Remmel, Minimal overlapping patterns for generalized Euler permutations, standard tableaux of rectangular shape, and column strict arrays, arXiv:1510.08190 [math.CO], 2015.

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 * A082480 A093934 A109458

Adjacent sequences:  A263864 A263865 A263866 * A263868 A263869 A263870

KEYWORD

nonn,more

AUTHOR

Sergi Elizalde, Oct 28 2015

STATUS

approved

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Last modified September 26 06:54 EDT 2017. Contains 292502 sequences.