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 A309563 #12 Aug 07 2019 21:12:38 %S A309563 1,1,1,1,2,3,2,2,4,6,2,2,6,8,4,4,6,10,4,4,10,12,4,4,12,18,6,6,8,12,8, %T A309563 8,16,22,6,6,18,22,8,8,12,22,10,10,22,26,8,8,20,32,12,12,18,24,12,12, %U A309563 28,36,8,8,30,38,16,16,20,36,16,16,24,30,12,12,36,54 %N A309563 Cyclic permutations of length n that avoid the patterns 123 and 231. %H A309563 Miklos Bona, Michael Cory, <a href="https://arxiv.org/abs/1805.05196">Cyclic Permutations Avoiding Pairs of Patterns of Length Three</a>, arXiv:1805.05196 [math.CO], 2018 %F A309563 a(2)=1; a(n)=phi(n/2) if n=4k, a(n)=phi((n+2)/4) +phi(n/2) if n=4k+2 > 2, and a(n)=phi((n+1)/2) if n is odd, where phi is the Euler totient function. %e A309563 a(4)=1, since the only cyclic permutation of length 4 avoiding both 123 and 231 is (4231)=4312. %Y A309563 Cf. A000010. %K A309563 nonn %O A309563 1,5 %A A309563 _Miklos Bona_, Aug 07 2019