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%I #36 Aug 13 2013 19:40:40
%S 1,1,2,5,16,62,284,1507,9104,61766
%N Number of equivalence classes of S_n under transformations of positionally adjacent elements of the form abc <--> acb where a<b<c.
%C Also number of equivalence classes of S_n under transformations of positionally adjacent elements of the form abc <--> bac where a<b<c.
%H Steven Linton, James Propp, Tom Roby, and Julian West, <a href="http://arxiv.org/abs/1111.3920"> Equivalence classes of permutations under various relations generated by constrained transpositions, 2011</a> arXiv:1111.3920 [math.CO]
%e From _Alois P. Heinz_, May 16 2012: (Start)
%e a(3) = 5: {123, 132}, {213}, {231}, {312}, {321}.
%e a(4) = 16: {1234, 1243, 1324, 1423}, {1342, 1432}, {2134, 2143}, {2314}, {2341, 2431}, {2413}, {3124, 3142}, {3214}, {3241}, {3412}, {3421}, {4123, 4132}, {4213}, {4231}, {4312}, {4321}. (End)
%Y Cf. A210668, A210669, A210671, A212417.
%K nonn
%O 0,3
%A _Tom Roby_, May 08 2012
%E Definition improved by _Tom Roby_, May 15 2012
%E a(0)-a(2), a(9) from _Alois P. Heinz_, May 16 2012