%I #12 Jan 19 2022 08:16:06
%S 4,0,12,0,96,1296,1520,23540,101472,686724
%N Number of circular permutations with no arithmetic progressions i, ..., i+r, ..., i+2r (mod n) of any equal spacings d.
%C Circular permutations are permutations whose indices are from the ring of integers modulo n. Here we count both the sequence 1,2,3 (r=1) as a progression in 1,2,3,0,4,5, (note d=1) and in 1,0,2,4,3,5 (here, d=2).
%H Peter Hegarty, <a href="https://doi.org/10.37236/1792">Permutations avoiding arithmetic patterns</a>, The Electronic Journal of Combinatorics, 11 (2004), #R39 (includes this sequence times n).
%e a(4) has the same value as A078628(4) since the only possible distance is 1.
%Y Cf. A078628, A174084, A174085, A174086.
%K nonn,more
%O 4,1
%A _Isaac Lambert_, Apr 20 2010