A165963
Number of permutations of length n without increasing or decreasing modular 3-sequences.
Original entry on oeis.org
0, 16, 80, 516, 3794, 31456, 290970, 2974380, 33311520, 405773448, 5342413414, 75612301688
Offset: 3
For n=4 there are a(4)=16 solutions, thus there are 4!-a(4)=8 permutations of length 4 with increasing or decreasing modular 3-sequences. These are the permutations (0,1,2,3), (0,3,2,1), (1,2,3,0), (1,0,3,2), (2,3,0,1), (2,1,0,3), (3,0,1,2), and (3,2,1,0).
A078603
Number of ways of arranging the numbers 1..n in a circle so that adjacent numbers do not differ by 1 mod n.
Original entry on oeis.org
1, 0, 0, 0, 2, 6, 46, 354, 3106, 29926, 315862, 3628906, 45132474, 604534846, 8680957902, 133082437730, 2169964347282, 37505486702678, 685046187718022, 13186335387855770, 266816610979894058, 5662225862272325550
Offset: 1
a(5) = 2: 1 3 5 2 4, 1 4 2 5 3; a(6) = 6: 1 4 6 2 5 3, 1 5 2 4 6 3, 1 5 3 6 2 4, 1 3 6 4 2 5, 1 4 2 6 3 5, 1 3 5 2 6 4.
The sequence was missing a zero; also added a cross-reference
Joel B. Lewis, Jan 28 2010
A174079
Number of circular permutations of length n with no consecutive triples i,i+2,i+4 (mod n) or i,i-2,i-4 (mod n).
Original entry on oeis.org
12, 84, 494, 3696, 30574
Offset: 5
For n=5 there are (5-1)!-a(5)=12 circular permutations with triples i,i+2,i+4 (mod 5) or triples i,i-2,i-4 (mod 5). An example of one is (0,3,1,2,4) because of the progression 0,3,1 (mod 5).
A174082
Number of circular permutations of (0,1,...,n-1) with no consecutive triples i,i+d,i+2d for all d>0.
Original entry on oeis.org
1, 1, 1, 5, 18, 91, 544, 3842, 30573, 277532, 2770405, 30591153, 366836571, 4783219673, 66906770461, 1006000805687
Offset: 1
For n=4 there is only (4-1)!-a(4) = 1 circular permutation with a consecutive triple i,i+d,i+2d. It is (0,1,2,3).
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.
Comments