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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).
4
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
3,5
REFERENCES
Wayne M. Dymacek, Isaac Lambert and Kyle Parsons, Arithmetic Progressions in Permutations, http://math.ku.edu/~ilambert/CN.pdf, 2012.
EXAMPLE
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;
...
CROSSREFS
Columns 1..2 are A165962, A216723.
Row sums are A000142(n-1).
Sequence in context: A325817 A325967 A229656 * A368865 A036297 A336530
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Sep 15 2012
STATUS
approved