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 A309508 #46 May 08 2025 02:21:09 %S A309508 1,1,1,2,4,10,24,66,178,512,1486,4446,13468,41648,130178,412670, %T A309508 1321418,4274970,13948966,45890440,152061154,507292698,1702753462, %U A309508 5748085332,19506240462 %N A309508 Number of cyclic permutations of length n avoiding the pattern 321. %C A309508 Comment from _F. Chapoton_, Sep 14 2021: (Start) %C A309508 The maps sending a permutation to its inverse or to its reverse-complement define two commuting involutions on these sets of permutations. %C A309508 The next terms in the sequence could be 41648, 130178, though these are counting Dyck words such that an associated permutation is cyclic, related but not obviously equivalent combinatorial objects. (End) %H A309508 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 A309508 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 A309508 For n=3, there are two such permutations, 231 and 312. %e A309508 The a(4) = 4 permutations are: 2341, 2413, 3142, 4123. %e A309508 The a(5) = 10 permutations are: 23451, 23514, 24153, 25134, 31452, 31524, 34512, 41253, 45123, 51234. %o A309508 (PARI) \\ See PARI link in A309504 for program code. %o A309508 for(n=0, 16, print1(E321(n), ", ")) \\ _Andrew Howroyd_, Nov 20 2024 %Y A309508 Cf. A000108 (number of permutations avoiding 321). %Y A309508 Cf. A000957, A309504, A309505, A309506. %K A309508 nonn,more %O A309508 0,4 %A A309508 _Miklos Bona_, Aug 05 2019 %E A309508 a(0)=1 prepended and a(13)-a(24) from _Andrew Howroyd_, Nov 17 2024