A309505 Number of cyclic permutations of length n that avoid the pattern 132 (equivalently, 213).

1, 1, 1, 2, 4, 10, 24, 68, 182, 544, 1574, 4888, 14864, 47610, 149964, 491802, 1592198, 5318936, 17593170, 59679516, 200805614, 689988886, 2354489616, 8178944510, 28240716098

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: 2341, 3421, 4123, 4312.
The a(5) = 10 permutations are: 23451, 34251, 34512, 43521, 45123, 45231, 51234, 53124, 53412, 54213.
		

Links

• Kassie Archer, Christina Graves, and Robert Laudone, Binary operations on pattern-avoiding cycles, arXiv:2505.04456 [math.CO], 2025.
• Miklos Bona and Michael Cory, Cyclic Permutations Avoiding Pairs of Patterns of Length Three, arXiv:1805.05196 [math.CO], 2018.
• Brice Huang, An Upper Bound on the Number of (132,213)-Avoiding Cyclic Permutations, arXiv:1808.08462 [math.CO], 2018-2019.

Crossrefs

Cf. A000108 (number of permutations avoiding 132).

Cf. A309504, A309506, A309508.

Programs

PARI

\\ See PARI link in A309504 for program code.
for(n=1, 16, print1(E213(n), ", ")) \\ Andrew Howroyd, Nov 20 2024

Extensions

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