A216718 Triangle read by rows: number of circular permutations of [1..n] with k progressions of rise 1, distance 1 and length 3 (n >= 3, k >= 0).

1, 1, 1, 5, 0, 1, 20, 3, 0, 1, 102, 14, 3, 0, 1, 627, 72, 17, 3, 0, 1, 4461, 468, 87, 20, 3, 0, 1, 36155, 3453, 582, 103, 23, 3, 0, 1, 328849, 28782, 4395, 704, 120, 26, 3, 0, 1, 3317272, 267831, 37257, 5435, 834, 138, 29, 3, 0, 1

Offset

2,4

References

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

Links

Table of n, a(n) for n=2..56.

Example

Triangle begins:
        1;
        1,      1; [this is row n=3]
        5,      0,     1;
       20,      3,     0,    1;
      102,     14,     3,    0,   1;
      627,     72,    17,    3,   0,   1;
     4461,    468,    87,   20,   3,   0,  1;
    36155,   3453,   582,  103,  23,   3,  0, 1;
   328849,  28782,  4395,  704, 120,  26,  3, 0, 1;
  3317272, 267831, 37257, 5435, 834, 138, 29, 3, 0, 1;
  ...

Crossrefs

Cf. A216716, A174072, A165961, A180187.

Sequence in context: A064315 A371994 A227322 * A184180 A256069 A356652

Adjacent sequences: A216715 A216716 A216717 * A216719 A216720 A216721

Keyword

nonn,tabl

Author

N. J. A. Sloane, Sep 15 2012

Extensions

a(2,0)=1 added by N. J. A. Sloane, Apr 16 2021

Status

approved