A174074 Number of circular permutations of length n without consecutive triples i,i+2,i+4.

1, 1, 1, 2, 6, 22, 109, 657, 4625, 37186, 336336, 3379058, 37328103, 449669577, 5866178493, 82387080624, 1239364493118, 19881771085788, 338797668091565, 6111688544942463, 116354993433563797, 2331395107113471188, 49042688584011866880, 1080639600739277669092, 24891049832682424745839

Offset

0,4

Comments

Circular permutations are permutations whose indices are from the ring of integers modulo n.

References

Wayne M. Dymacek, Isaac Lambert and Kyle Parsons, Arithmetic Progressions in Permutations, http://math.ku.edu/~ilambert/CN.pdf, 2012.

Links

Max Alekseyev, Table of n, a(n) for n = 0..100

Kyle Parsons, Arithmetic Progressions in Permutations, thesis, 2011. See Table 3, p. 9.

Example

Since a(5)=22, there are (5-1)!-22=2 circular permutations with consecutive triples i,i+2,i+4 in all circular permutations of length 5. They are exactly (0,2,4,1,3) and (0,2,4,3,1).

Crossrefs

Column 1 of A216719.

Cf. A165961, A174072, A174073, A174075.

Sequence in context: A129535 A375131 A216720 * A290279 A014371 A374618

Adjacent sequences: A174071 A174072 A174073 * A174075 A174076 A174077

Keyword

nonn

Author

Isaac Lambert, Mar 06 2010

Extensions

a(10)-a(15) from Donovan Johnson, Sep 24 2010

a(0)-a(2) prepended and terms a(16) onward added by Max Alekseyev, Feb 04 2024

Status

approved