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 A309504 #34 May 08 2025 15:27:15 %S A309504 1,1,1,2,4,10,24,68,188,586,1722,5492,16924,55582,177278,594460, %T A309504 1944980,6628384,22132112,76421498,259359036,905416294,3114033930, %U A309504 10971347070,38157201530 %N A309504 Number of cyclic permutations of length n avoiding the pattern 123. %H A309504 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 A309504 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 A309504 Andrew Howroyd, <a href="/A309504/a309504.txt">PARI Program</a>, Nov 2024. %e A309504 For n=3, there are two such permutations, 231 and 312. %e A309504 The a(4) = 4 permutations are: 2413, 3142, 3421, 4312. %e A309504 The a(5) = 10 permutations are: 25413, 35214, 35421, 41532, 43152, 43521, 45231, 53412, 54132, 54213. %o A309504 (PARI) \\ See Links for program code. %o A309504 for(n=0, 16, print1(E123(n), ", ")) \\ _Andrew Howroyd_, Nov 20 2024 %Y A309504 Cf. A000108 (number of permutations avoiding 123). %Y A309504 Cf. A309505, A309506, A309508. %K A309504 nonn,more %O A309504 0,4 %A A309504 _Miklos Bona_, Aug 05 2019 %E A309504 a(0)=1 prepended and a(13)-a(24) from _Andrew Howroyd_, Nov 17 2024