A235943 Number a(n,k) of positions (cyclic permutations) of circular permutations of [n] with exactly k (unspecified) increasing or decreasing modular runs (3-sequences), with clockwise and counterclockwise traversals counted as distinct; triangle a(n,k) read by rows, 0<=k<=n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 16, 0, 0, 0, 8, 60, 50, 0, 0, 0, 10, 456, 144, 108, 0, 0, 0, 12, 3458, 1078, 294, 196, 0, 0, 0, 14, 29296, 7936, 2240, 512, 320, 0, 0, 0, 16, 275166, 66096, 16200, 4104, 810, 486, 0, 0, 0, 18, 2843980, 611200, 135600, 29200, 6900, 1200, 700, 0, 0, 0, 20

Offset

0,10

Comments

Arrangements that differ in the direction in which the cycle is traversed count as different.

References

Paul J. Campbell, Circular permutations with exactly one modular run (3-sequence), submitted to Journal of Integer Sequences

Links

Paul J. Campbell, Rows n = 0..13, flattened

Paul J. Campbell, Table of rows n = 0..13 of A235943

Wayne M. Dymáček and Isaac Lambert, Circular permutations avoiding runs of i, i+1, i+2 or i, i-1, i-2, Journal of Integer Sequences, Vol. 14 (2011) Article 11.1.6.

Crossrefs

Cf. A165961, A165964, A165962, A078628, A078673.

Cf. A235937, A235938, A235939, A235940, A235941, A235942.

Sequence in context: A354682 A280964 A191463 * A225304 A299709 A107777

Adjacent sequences: A235940 A235941 A235942 * A235944 A235945 A235946

Keyword

nonn,tabl

Author

Paul J. Campbell, Jan 20 2014, with Joe Marasco and Ashish Vikram

Status

approved