The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #25 Nov 20 2024 16:26:25
%S 1,1,1,2,4,10,24,68,182,544,1574,4888,14864,47610,149964,491802,
%T 1592198,5318936,17593170,59679516,200805614,689988886,2354489616,
%U 8178944510,28240716098
%N Number of cyclic permutations of length n that avoid the pattern 132 (equivalently, 213).
%H Miklos Bona, Michael Cory, <a href="http://arxiv.org/abs/1805.05196">Cyclic Permutations Avoiding Pairs of Patterns of Length Three</a>, arXiv:1805.05196 [math.CO], 2018.
%H Brice Huang, <a href="https://arxiv.org/abs/1808.08462">An Upper Bound on the Number of (132,213)-Avoiding Cyclic Permutations</a>, arXiv:1808.08462 [math.CO], 2018-2019.
%e For n=3, there are two such permutations, 231 and 312.
%e The a(4) = 4 permutations are: 2341, 3421, 4123, 4312.
%e The a(5) = 10 permutations are: 23451, 34251, 34512, 43521, 45123, 45231, 51234, 53124, 53412, 54213.
%o (PARI) \\ See PARI link in A309504 for program code.
%o for(n=1, 16, print1(E213(n), ", ")) \\ _Andrew Howroyd_, Nov 20 2024
%Y Cf. A000108 (number of permutations avoiding 132).
%Y Cf. A309504, A309506, A309508.
%K nonn,more,changed
%O 0,4
%A _Miklos Bona_, Aug 05 2019
%E a(0)=1 prepended and a(13)-a(24) from _Andrew Howroyd_, Nov 20 2024