A216719 Triangle read by rows: number of circular permutations of [1..n] with k progressions of rise 1, distance 2 and length 3 (n >= 3, k >= 0).

2, 6, 22, 2, 109, 10, 1, 657, 55, 7, 1, 4625, 356, 54, 4, 1, 37186, 2723, 362, 44, 4, 1, 336336, 23300, 2837, 368, 34, 4, 1, 3379058, 220997, 25408, 2967, 330, 35, 4, 1, 37328103, 2308564, 249736, 26964, 3100, 292, 36, 4, 1

Offset

3,1

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=3..48.

Example

Triangle begins:
         2
         6
        22       2
       109      10      1
       657      55      7     1
      4625     356     54     4    1
     37186    2723    362    44    4   1
    336336   23300   2837   368   34   4  1
   3379058  220997  25408  2967  330  35  4 1
  37328103 2308564 249736 26964 3100 292 36 4 1
  ...

Crossrefs

Columns 1..2 are A174074, A216721.

Row sums are A000142(n-1).

Cf. A216716, A216718.

Sequence in context: A216964 A187250 A129534 * A085286 A062085 A284632

Adjacent sequences: A216716 A216717 A216718 * A216720 A216721 A216722

Keyword

nonn,tabf

Author

N. J. A. Sloane, Sep 15 2012

Status

approved