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A342853 Maximal number of 1324 patterns in a permutation of 1,2,...,n.

%I A342853 #31 Feb 16 2025 08:34:01
%S A342853 0,0,0,0,1,3,6,13,24,42,68,106,153,217,300
%N A342853 Maximal number of 1324 patterns in a permutation of 1,2,...,n.
%C A342853 Equivalently the maximal number of 4231 patterns in a permutation of 1,2,...,n.
%H A342853 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 A342853 Miklós Bóna. <a href="https://doi.org/10.1007/s40879-014-0020-6">A new record for 1324-avoiding permutations</a> European Journal of Mathematics 1 (2015), 198-206.
%H A342853 Anders Claesson, Vít Jelínek, and Einar Steingrímsson, <a href="https://doi.org/10.1016/j.jcta.2012.05.006">Upper bounds for the Stanley-Wilf limit of 1324 and other layered patterns</a>, Journal of Combinatorial Theory, Series A, 199.8 (2012), 1680-1691.
%H A342853 FindStat, <a href="http://www.findstat.org/StatisticsDatabase/St000405">St000405: The number of occurrences of the pattern 1324 in a permutation.</a>
%H A342853 User Noodle9, answer to <a href="https://codegolf.stackexchange.com/a/221389/53884">Patterns in Permutations</a>, Code Golf Stack Exchange.
%H A342853 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PermutationPattern.html">Permutation Pattern</a>
%e A342853 For n = 5, the permutation 14325 has a(5) = 3 subsequences with the same relative order as 1324: 1435, 1425, and 1325.
%e A342853 All other permutations in S_5 have 3 or fewer such subsequences.
%Y A342853 Analogous for other patterns: A000292 (123), A000332 (1234), A061061 (132), A100354 (1432), A342646 (4213), A342854 (2413).
%K A342853 nonn,more
%O A342853 0,6
%A A342853 _Peter Kagey_, Mar 25 2021
%E A342853 a(11) from Code Golf Stack Exchange link added by _Peter Kagey_, Mar 25 2021
%E A342853 a(12)-a(14) from _Hugo Pfoertner_, Mar 26 2021