Rupert Li - cp's OEIS frontend

User: Rupert Li

Rupert Li has authored 2 sequences.

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

Rupert Li, Aug 03 2021

nonn

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.

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.

Cf. A025242, A047970, A346660.

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

A346660 Number of cyclic patterns of length n that avoid the vincular pattern 23-1-4.

Original entry on oeis.org

1, 1, 1, 2, 5, 14, 42, 133, 442, 1537, 5583, 21165, 83707, 345324, 1485687, 6663354, 31134078, 151408319, 765462514, 4017644518, 21860398111, 123120413119, 716701884408, 4305828784896, 26661920519485, 169937265101628, 1113616036893636, 7494786443901137

Offset: 0

Rupert Li, Aug 03 2021

nonn

The vincular pattern 23-1-4 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 32-4-1.

Vaclav Kotesovec, Table of n, a(n) for n = 0..500
Rupert Li, Vincular Pattern Avoidance on Cyclic Permutations, arXiv:2107.12353 [math.CO], 2021.

Cf. A025242, A047970, A092920, A346661.

For n >= 2, a(n) = Sum_{i=0..n-2} binomial(n-2,i) * A092920(i).

cp's OEIS Frontend

User: Rupert Li

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

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