This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A342646 #62 Feb 16 2025 08:34:01 %S A342646 0,0,0,0,1,3,6,13,24,40,62,96,138,192,264,354 %N A342646 Maximal number of 4213 patterns in a permutation of 1,2,...,n. %C A342646 Equivalently the maximal number of 1342, 2431, and 3124 patterns. %H A342646 M. H. Albert, M. D. Atkinson, C. C.Handley, D. A. Holton, and W. Stromquist, <a href="https://doi.org/10.37236/1622">On packing densities of permutations</a>, The Electronic Journal of Combinatorics, 9(1) (2002). %H A342646 David Bevan, <a href="http://arxiv.org/abs/1510.06328">The permutation class Av(4213,2143)</a>, arXiv:1510.06328 [math.CO], 2015. %H A342646 FindStat, <a href="http://www.findstat.org/StatisticsDatabase/St000750">St000750: The number of occurrences of the pattern 4213 in a permutation.</a> %H A342646 Rob Pratt, <a href="https://math.stackexchange.com/a/4071338/121988">Greatest number of occurrences of the pattern 4213 in a permutation</a>, Mathematics Stack Exchange. %H A342646 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PermutationPattern.html">Permutation Pattern</a> %e A342646 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. %e A342646 Moreover, all other permutations in S_7 have 13 or fewer instances of this pattern. %Y A342646 Analogous for other patterns: A000292 (123), A000332 (1234), A061061 (132), A100354 (1432). %Y A342646 Cf. A005802, A022558 %K A342646 nonn,more %O A342646 0,6 %A A342646 _Peter Kagey_, Mar 20 2021 %E A342646 a(10)-a(12) from _Rob Pratt_ %E A342646 a(13)-a(15) from _Bert Dobbelaere_, Mar 26 2021