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

Author

Isaac Lambert, Mar 06 2010

Keywords

• nonn

Comments

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

Examples

			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).
		

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.

Crossrefs

Column 1 of A216719.

Cf. A165961, A174072, A174073, A174075.

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