A309506 Number of cyclic permutations of length n avoiding the pattern 231 (equivalently, 312).

1, 1, 1, 1, 2, 5, 12, 30, 86, 253, 748, 2274, 7152, 22890, 74189, 243342, 808599, 2716549, 9213420, 31498358, 108483093, 376145636, 1312463081, 4605569378, 16245866825

Offset: 0

Author

Miklos Bona, Aug 05 2019

Keywords

• nonn
• more

Examples

			For n=4, there are two such permutations, 4123 and 4312.
The a(5) = 5 permutations are 51234, 51423, 53124, 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.

Crossrefs

Cf. A000108 (number of permutations avoiding 231).

Cf. A309504, A309505, A309508.

Programs

PARI

\\ See PARI link in A309504 for program code.
for(n=0, 16, print1(E231(n), ", ")) \\ Andrew Howroyd, Nov 20 2024

Extensions

a(1)=1 (confirmed by author) inserted by Alexander Burstein, Jul 20 2020

a(0)=1 prepended and a(13)-a(24) from Andrew Howroyd, Nov 20 2024