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.
A174085
Number of permutations of length n with no consecutive triples i,...i+r,...i+2r for all positive and negative r, and for all equal spacings d.
Original entry on oeis.org
1, 1, 2, 4, 18, 72, 396, 2328, 17050, 131764, 1199368, 11379524, 123012492, 1386127700, 17450444866, 227152227940
Offset: 0
a(3) = 4; 123 and 321 each contain a 3-term arithmetic progression.
Since the only possibilities for progressions for n=4 are d=1 and r=1 and -1, we get the same term as A095816(4).
Cf.
A179040 (number of permutations of 1..n with no three elements collinear).
Cf.
A003407 for another interpretation of avoiding 3-term APs.
a(0)-a(3) and a(10)-a(13) from
David Bevan, Jun 16 2021
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).
Showing 1-3 of 3 results.
Comments