A309504 Number of cyclic permutations of length n avoiding the pattern 123.

1, 1, 1, 2, 4, 10, 24, 68, 188, 586, 1722, 5492, 16924, 55582, 177278, 594460, 1944980, 6628384, 22132112, 76421498, 259359036, 905416294, 3114033930, 10971347070, 38157201530

Offset: 0

Author

Miklos Bona, Aug 05 2019

Keywords

• nonn
• more

Examples

			For n=3, there are two such permutations, 231 and 312.
The a(4) = 4 permutations are: 2413, 3142, 3421, 4312.
The a(5) = 10 permutations are: 25413, 35214, 35421, 41532, 43152, 43521, 45231, 53412, 54132, 54213.
		

Links

• Kassie Archer, Christina Graves, and Robert Laudone, Binary operations on pattern-avoiding cycles, arXiv:2505.04456 [math.CO], 2025. See p. 23.
• Miklos Bona and Michael Cory, Cyclic Permutations Avoiding Pairs of Patterns of Length Three, arXiv:1805.05196 [math.CO], 2018.
• Andrew Howroyd, PARI Program, Nov 2024.

Crossrefs

Cf. A000108 (number of permutations avoiding 123).

Cf. A309505, A309506, A309508.

Programs

PARI

\\ See Links for program code.
for(n=0, 16, print1(E123(n), ", ")) \\ Andrew Howroyd, Nov 20 2024

Extensions

a(0)=1 prepended and a(13)-a(24) from Andrew Howroyd, Nov 17 2024