A342854 Maximal number of 2413 patterns in a permutation of 1,2,...,n.

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

Offset: 0

Author

Peter Kagey, Mar 25 2021

Keywords

• nonn
• more

Comments

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

Examples

			For n = 6, the permutation 246135 has a(6) = 5 subsequences with the same relative order as 2413: 2413, 2613, 2615, 4615, and 4635.
All other permutations in S_6 have 5 or fewer such subsequences.
		

Links

• 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).
• Eric Weisstein's World of Mathematics, Permutation Pattern

Crossrefs

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

Cf. A342860.

Extensions

a(11)-a(14) from Hugo Pfoertner, Mar 26 2021

a(15) from Hugo Pfoertner, Apr 05 2021