A174087 Number of circular permutations with no arithmetic progressions i, ..., i+r, ..., i+2r (mod n) of any equal spacings d.

4, 0, 12, 0, 96, 1296, 1520, 23540, 101472, 686724

Offset: 4

Author

Isaac Lambert, Apr 20 2010

Keywords

• nonn
• more

Comments

Circular permutations are permutations whose indices are from the ring of integers modulo n. Here we count both the sequence 1,2,3 (r=1) as a progression in 1,2,3,0,4,5, (note d=1) and in 1,0,2,4,3,5 (here, d=2).

Examples

			a(4) has the same value as A078628(4) since the only possible distance is 1.
		

Links

• Peter Hegarty, Permutations avoiding arithmetic patterns, The Electronic Journal of Combinatorics, 11 (2004), #R39 (includes this sequence times n).

Crossrefs

Cf. A078628, A174084, A174085, A174086.