A346661 Number of cyclic patterns of length n that avoid the vincular pattern 23-4-1.

1, 1, 2, 5, 15, 50, 180, 690, 2792, 11857, 52633, 243455, 1170525, 5837934, 30151474, 161021581, 888001485, 5051014786, 29600662480, 178541105770, 1107321666920, 7055339825171, 46142654894331, 309513540865544, 2127744119042216, 14979904453920111, 107932371558460341, 795363217306369817, 5990768203554158167, 46094392105916344968, 362092868720288824992

Offset

0,3

Comments

The vincular pattern 23-4-1 requires the 2 and the 3 to be adjacent.

By the trivial Wilf equivalence obtained by reversing the permutations, a(n) is also the number of cyclic patterns of length n that avoid the vincular pattern 32-1-4.

Links

Table of n, a(n) for n=0..30.

Rupert Li, Vincular Pattern Avoidance on Cyclic Permutations, arXiv:2107.12353 [math.CO], 2021.

Toufik Mansour and Mark Shattuck, Enumerating circular permutations avoiding the vincular pattern 23 4 1, arXiv:2111.04211 [math.CO], 2021.

Toufik Mansour and Mark Shattuck, On a question of Li concerning an uncounted class of circular permutations, The Australasian Journal of Combinatorics, volume 83 part 1, 2022, pp. 176-195.

Crossrefs

Cf. A025242, A047970, A346660.

Sequence in context: A337522 A149952 A337526 * A060049 A107590 A245311

Adjacent sequences: A346658 A346659 A346660 * A346662 A346663 A346664

Keyword

nonn

Author

Rupert Li, Aug 03 2021

Extensions

More terms from Vaclav Kotesovec, Nov 09 2021, computed by Toufik Mansour and Mark Shattuck

Status

approved