A165960
Number of permutations of length n without modular 3-sequences.
Original entry on oeis.org
1, 1, 2, 3, 20, 100, 612, 4389, 35688, 325395, 3288490, 36489992, 441093864, 5770007009, 81213878830, 1223895060315, 19662509071056, 335472890422812, 6057979285535388, 115434096553014565, 2314691409652237700, 48723117262650147387, 1074208020519710570054
Offset: 0
For n=3 the a(3) = 3 solutions are (0,2,1), (1,0,2) and (2,1,0).
A216722
Triangle read by rows: number of circular permutations of [1..n] with k modular progressions of rise 1, distance 1 and length 3 (n >= 3, 0 <= k <= n).
Original entry on oeis.org
1, 0, 0, 1, 5, 0, 0, 0, 1, 18, 5, 0, 0, 0, 1, 95, 18, 6, 0, 0, 0, 1, 600, 84, 28, 7, 0, 0, 0, 1, 4307, 568, 116, 40, 8, 0, 0, 0, 1, 35168, 4122, 810, 156, 54, 9, 0, 0, 0, 1, 321609, 33910, 5975, 1100, 205, 70, 10, 0, 0, 0, 1
Offset: 3
Triangle begins:
1, 0, 0, 1;
5, 0, 0, 0, 1;
18, 5, 0, 0, 0, 1;
95, 18, 6, 0, 0, 0, 1;
600, 84, 28, 7, 0, 0, 0, 1;
4307, 568, 116, 40, 8, 0, 0, 0, 1;
35168, 4122, 810, 156, 54, 9, 0, 0, 0, 1;
321609, 33910, 5975, 1100, 205, 70, 10, 0, 0, 0, 1;
...
- Wayne M. Dymacek, Isaac Lambert and Kyle Parsons, Arithmetic Progressions in Permutations, http://math.ku.edu/~ilambert/CN.pdf, 2012.
A174083
Number of circular permutations of length n with no consecutive triples (i, i+d, i+2d) (mod n) for all d.
Original entry on oeis.org
4, 0, 40, 168, 1652, 9408, 117896, 1019260, 12737856, 140794368, 2072921376, 25990014896, 439692361160
Offset: 4
For n=5 since a(5)=0 all (5-1)! = 24 circular permutations of length 5 have some consecutive triple (i, i+d, i+2d) (mod 5). For example, the permutation (0,4,2,1,3) has a triple (1,3,0) with d=2. This is clearly a special case.
Original entry on oeis.org
0, 0, 5, 18, 84, 568, 4122, 33910
Offset: 3
- Wayne M. Dymacek, Isaac Lambert and Kyle Parsons, Arithmetic Progressions in Permutations, http://math.ku.edu/~ilambert/CN.pdf, 2012.
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