This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A309505 #30 May 08 2025 02:20:40 %S A309505 1,1,1,2,4,10,24,68,182,544,1574,4888,14864,47610,149964,491802, %T A309505 1592198,5318936,17593170,59679516,200805614,689988886,2354489616, %U A309505 8178944510,28240716098 %N A309505 Number of cyclic permutations of length n that avoid the pattern 132 (equivalently, 213). %H A309505 Kassie Archer, Christina Graves, and Robert Laudone, <a href="https://arxiv.org/abs/2505.04456">Binary operations on pattern-avoiding cycles</a>, arXiv:2505.04456 [math.CO], 2025. %H A309505 Miklos Bona and 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 A309505 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 A309505 For n=3, there are two such permutations, 231 and 312. %e A309505 The a(4) = 4 permutations are: 2341, 3421, 4123, 4312. %e A309505 The a(5) = 10 permutations are: 23451, 34251, 34512, 43521, 45123, 45231, 51234, 53124, 53412, 54213. %o A309505 (PARI) \\ See PARI link in A309504 for program code. %o A309505 for(n=1, 16, print1(E213(n), ", ")) \\ _Andrew Howroyd_, Nov 20 2024 %Y A309505 Cf. A000108 (number of permutations avoiding 132). %Y A309505 Cf. A309504, A309506, A309508. %K A309505 nonn,more %O A309505 0,4 %A A309505 _Miklos Bona_, Aug 05 2019 %E A309505 a(0)=1 prepended and a(13)-a(24) from _Andrew Howroyd_, Nov 20 2024