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

4,1

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).

Links

Table of n, a(n) for n=4..13.

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

Example

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

Crossrefs

Cf. A078628, A174084, A174085, A174086.

Sequence in context: A349711 A167296 A147607 * A072194 A225952 A273795

Adjacent sequences: A174084 A174085 A174086 * A174088 A174089 A174090

Keyword

nonn,more

Author

Isaac Lambert, Apr 20 2010

Status

approved