

A235943


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


7



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
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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 (3sequence), 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, i1, i2, 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: A280964 A191463 A068941 * 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



