A174084
Number of permutations of length n with no consecutive triples i,...i+r,...i+2r for all positive r, and for all equal spacings d.
Original entry on oeis.org
21, 94, 544, 3509, 26799, 223123, 2133511, 21793042, 248348572, 3008632130, 39989075942, 558800689295
Offset: 4
For n=4 there are 4!-a(4)=3 with some progression. These are (0,1,2,3), (1,2,3,0), and (3,0,1,2). Here for all the progressions, r=1 and d=1, hence this term is the same as a(4) in A002628.
A174086
Number of permutations of length n with no consecutive triples i,...i+r,...i+2r (mod n) for all r, and for all equal spacings d.
Original entry on oeis.org
16, 40, 204, 840, 6272, 35856, 378000, 2638460, 28387728, 249444936, 3275745564, 30770034480
Offset: 4
For n=4 note a(4) is the same as the value in A165963 since there are no other distances that can be used (i.e. only d=1).
A174087
Number of circular permutations with no arithmetic progressions i, ..., i+r, ..., i+2r (mod n) of any equal spacings d.
Original entry on oeis.org
4, 0, 12, 0, 96, 1296, 1520, 23540, 101472, 686724
Offset: 4
a(4) has the same value as A078628(4) since the only possible distance is 1.
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