login
A235937
Number of circular permutations with exactly one specified increasing or decreasing modular run (3-sequence), 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
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 {n-1,n} but have no increasing or decreasing 3-sequence, viz., the sequence b(0,1...n-2,n-1) in Dymáček and Lambert.
REFERENCES
Paul J. Campbell, Circular permutations with exactly one modular run (3-sequence), submitted to Journal of Integer Sequences
LINKS
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.
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.
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 b-file deleted by N. J. A. Sloane, Jan 05 2019
STATUS
approved