

A235937


Number of circular permutations with exactly one specified increasing or decreasing modular run (3sequence), with clockwise and counterclockwise traversals not counted as distinct.


6



0, 0, 0, 0, 1, 2, 11, 62, 408, 3056, 25821, 242802, 2517303, 28540102, 351383192, 4669815008, 66640974977, 1016522211474, 16507095990251, 284343231536742, 5178919228252440
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OFFSET

1,6


COMMENTS

Arrangements that differ only in the direction in which the cycle is traversed do not count as different.
This sequence is the same as for straight permutations of {0,1,...,n} that begin with {0,1} and end with {n1,n} but have no increasing or decreasing 3sequence, viz., the sequence b(0,1...n2,n1) in Dymáček and Lambert.


REFERENCES

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


LINKS

Table of n, a(n) for n=1..21.
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.


EXAMPLE

With specified sequence 123:
a(5) = 1: 12354.
a(6) = 2: 123564, 123645.
a(7) = 11: 1235476, 1235746, 1235764, 1236475, 1236574, 1236745, 1236754, 1237465, 1237546, 1237564, 1237645.


CROSSREFS

Cf. A165961, A165964, A165962, A078628, A078673.
Cf. A235938, A235939, A235940, A235941, A235942, A235943.
Sequence in context: A183160 A020078 A002629 * A065928 A188648 A114175
Adjacent sequences: A235934 A235935 A235936 * A235938 A235939 A235940


KEYWORD

nonn


AUTHOR

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


EXTENSIONS

a(20)a(21) from Alois P. Heinz, Jan 24 2014
Obsolete bfile deleted by N. J. A. Sloane, Jan 05 2019


STATUS

approved



