A235939 Number of circular permutations with exactly one (unspecified) increasing or decreasing modular 3-sequence, with clockwise and counterclockwise traversals not counted as distinct.

0, 0, 0, 0, 5, 12, 77, 496, 3672, 30560, 284031, 2913624, 32724939, 399561428, 5270747880, 74717040128, 1132896574609, 18297399806532, 313634823814769, 5686864630734840, 108757303793301240

Offset

1,5

Comments

Arrangements that differ only in the direction in which the cycle is traversed do not count as different.

References

Paul J. Campbell, Circular permutations with exactly one modular run (3-sequence), 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, i-1, i-2, Journal of Integer Sequences, Vol. 14 (2011) Article 11.1.6.

Formula

a(n) = n*A235937(n).

Example

a(5) = 5: 12354, 23415, 34521, 45132, 51243.

Crossrefs

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

Cf. A235937, A235938, A235940, A235941, A235942, A235943.

Sequence in context: A128323 A202203 A074245 * A215866 A219288 A368074

Adjacent sequences: A235936 A235937 A235938 * A235940 A235941 A235942

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