A342646 Maximal number of 4213 patterns in a permutation of 1,2,...,n.

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

Table of n, a(n) for n=0..15.

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.

FindStat, St000750: The number of occurrences of the pattern 4213 in a permutation.

Rob Pratt, Greatest number of occurrences of the pattern 4213 in a permutation, Mathematics Stack Exchange.

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).

Cf. A005802, A022558

Sequence in context: A162426 A374627 A058554 * A342853 A128517 A022568

Adjacent sequences: A342643 A342644 A342645 * A342647 A342648 A342649

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