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).

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

Author

N. J. A. Sloane, Sep 15 2012

Keywords

• nonn
• tabf

Examples

			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;
  ...
		

References

• Wayne M. Dymacek, Isaac Lambert and Kyle Parsons, Arithmetic Progressions in Permutations, http://math.ku.edu/~ilambert/CN.pdf, 2012.

Crossrefs

Columns 1..2 are A165962, A216723.

Row sums are A000142(n-1).

Cf. A216716, A216718, A216719, A165962.