A342646 - OEIS

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

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

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