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

Author

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

Keywords

• nonn

Comments

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

Examples

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

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.

Crossrefs

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

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

Formula

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

Extensions

a(20)-a(21) from Alois P. Heinz, Jan 24 2014

Obsolete b-file deleted by N. J. A. Sloane, Jan 05 2019