A342854 - OEIS

%I #30 Apr 05 2021 03:53:16

%S 0,0,0,0,1,2,5,9,17,26,41,60,88,120,163,213

%N Maximal number of 2413 patterns in a permutation of 1,2,...,n.

%C Equivalently the maximal number of 3142 patterns in a permutation of 1,2,...,n.

%H 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PermutationPattern.html">Permutation Pattern</a>

%e For n = 6, the permutation 246135 has a(6) = 5 subsequences with the same relative order as 2413: 2413, 2613, 2615, 4615, and 4635.

%e All other permutations in S_6 have 5 or fewer such subsequences.

%Y Analogous for other patterns: A000292 (123), A000332 (1234), A061061 (132), A100354 (1432), A342646 (4213), A342853 (1324).

%Y Cf. A342860.

%K nonn,more

%O 0,6

%A _Peter Kagey_, Mar 25 2021

%E a(11)-a(14) from _Hugo Pfoertner_, Mar 26 2021

%E a(15) from _Hugo Pfoertner_, Apr 05 2021