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 A309506 #45 May 08 2025 15:27:31 %S A309506 1,1,1,1,2,5,12,30,86,253,748,2274,7152,22890,74189,243342,808599, %T A309506 2716549,9213420,31498358,108483093,376145636,1312463081,4605569378, %U A309506 16245866825 %N A309506 Number of cyclic permutations of length n avoiding the pattern 231 (equivalently, 312). %H A309506 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. See p. 23. %H A309506 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. %e A309506 For n=4, there are two such permutations, 4123 and 4312. %e A309506 The a(5) = 5 permutations are 51234, 51423, 53124, 54132, 54213. %o A309506 (PARI) \\ See PARI link in A309504 for program code. %o A309506 for(n=0, 16, print1(E231(n), ", ")) \\ _Andrew Howroyd_, Nov 20 2024 %Y A309506 Cf. A000108 (number of permutations avoiding 231). %Y A309506 Cf. A309504, A309505, A309508. %K A309506 nonn,more %O A309506 0,5 %A A309506 _Miklos Bona_, Aug 05 2019 %E A309506 a(1)=1 (confirmed by author) inserted by _Alexander Burstein_, Jul 20 2020 %E A309506 a(0)=1 prepended and a(13)-a(24) from _Andrew Howroyd_, Nov 20 2024