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

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

Author

Rupert Li, Aug 03 2021

Keywords

• nonn

Comments

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.

Links

• 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.

Crossrefs

Cf. A025242, A047970, A092920, A346661.

Formula

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