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A342646
Maximal number of 4213 patterns in a permutation of 1,2,...,n.
3
0, 0, 0, 0, 1, 3, 6, 13, 24, 40, 62, 96, 138, 192, 264, 354
OFFSET
0,6
COMMENTS
Equivalently the maximal number of 1342, 2431, and 3124 patterns.
LINKS
M. H. Albert, M. D. Atkinson, C. C.Handley, D. A. Holton, and W. Stromquist, On packing densities of permutations, The Electronic Journal of Combinatorics, 9(1) (2002).
David Bevan, The permutation class Av(4213,2143), arXiv:1510.06328 [math.CO], 2015.
Eric Weisstein's World of Mathematics, Permutation Pattern
EXAMPLE
For n = 7, a(7) = 13 because the permutation 7532146 has 13 instances of the pattern 4213, namely: 7536, 7526, 7516, 7546, 7324, 7326, 7314, 7316, 7214, 7216, 5324, 5314, and 5214.
Moreover, all other permutations in S_7 have 13 or fewer instances of this pattern.
CROSSREFS
Analogous for other patterns: A000292 (123), A000332 (1234), A061061 (132), A100354 (1432).
Sequence in context: A162426 A374627 A058554 * A342853 A128517 A022568
KEYWORD
nonn,more
AUTHOR
Peter Kagey, Mar 20 2021
EXTENSIONS
a(10)-a(12) from Rob Pratt
a(13)-a(15) from Bert Dobbelaere, Mar 26 2021
STATUS
approved