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 A260506 #9 Aug 19 2015 19:24:53 %S A260506 1,3,18,140,1384,16428,228248 %N A260506 Number of signed permutations of length n that are sortable to the identity permutation by some sequence of cdr (context-directed reversal) and cds (context-directed swap) moves. %C A260506 a(n) is equivalently the number of signed permutations such that in the reality-desire graph of the permutation, 0 and n are in different cycles. %C A260506 It is also the number of signed permutations such that the overlap of that permutation contains a partition into two vertex sets, V_1 and V_2, such that (i) vertices (0,1) and (n,n+1) are in different cycles, and (ii) every vertex in V_1 is adjacent to an even number of vertices in V_2, and every vertex in V_2 is adjacent to an even number of vertices in V_1. %C A260506 It is expected (but not proven) asymptotically that a(n) is about one-third of all permutations, i.e., it is about (2^n * n!) / 3. %H A260506 K. L. M. Adamyk, E. Holmes, G. R. Mayfield, D. J. Moritz, M. Scheepers, B. E. Tenner, and H. C. Wauck, <a href="http://arxiv.org/abs/1410.2353"> Sorting permutations: games, genomes, and cycles</a>, arXiv:1410.2353 [math.CO], 2014. %e A260506 a(2) = 3 because out of the 8 signed permutations of size 2, only [1,2], [1,-2], and [-1,2] are sortable. They each take one cdr move. Three other permutations, [-2,-1], [2,-1], and [-2,1] are not sortable to the identity [1,2] but instead sort to [-2,-1]. Finally, [2,1] and [-1,-2] sort to neither [1,2] nor [-2,-1]. %Y A260506 A249165 counts the special case of this property for unsigned permutations. Note that for unsigned permutations, there are no valid cdr moves, so sortability by cdr and cds is equivalent to sortability by cds only. %Y A260506 A000165 counts the total number of signed permutations. %K A260506 nonn,more %O A260506 1,2 %A A260506 _Caleb Stanford_, Jul 27 2015