A235938 Number of circular permutations with exactly one specified increasing or decreasing modular run (3-sequence), with clockwise and counterclockwise traversals counted as distinct.

0, 0, 0, 0, 2, 4, 22, 124, 816, 6112, 51642, 485604, 5034606, 57080204, 702766384, 9339630016, 133281949954, 2033044422948, 33014191980502, 568686463073484, 10357838456504880

Offset

1,5

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) = 2*A235937(n).

Example

With specified sequence 123:
a(5) = 2: 12354, 32154.
a(6) = 4: 123564, 321564, 123645, 321546.

Crossrefs

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

Cf. A235937, A235939, A235940, A235941, A235942, A235943.

Sequence in context: A366732 A165588 A289191 * A279705 A321248 A309741

Adjacent sequences: A235935 A235936 A235937 * A235939 A235940 A235941

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