|
| |
|
|
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
|
| |
|
|
|
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 * A326863 A082480 A093934
Adjacent sequences: A263864 A263865 A263866 * A263868 A263869 A263870
|
|
|
KEYWORD
|
nonn,more
|
|
|
AUTHOR
|
Sergi Elizalde, Oct 28 2015
|
|
|
STATUS
|
approved
|
| |
|
|
