A174084 Number of permutations of length n with no consecutive triples i,...i+r,...i+2r for all positive r, and for all equal spacings d.

21, 94, 544, 3509, 26799, 223123, 2133511, 21793042, 248348572, 3008632130, 39989075942, 558800689295

Offset: 4

Author

Isaac Lambert, Apr 20 2010

Keywords

• nonn
• more

Comments

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

			For n=4 there are 4!-a(4)=3 with some progression. These are (0,1,2,3), (1,2,3,0), and (3,0,1,2). Here for all the progressions, r=1 and d=1, hence this term is the same as a(4) in A002628.
		

Crossrefs

Cf. A002628, A174080, A174085, A174086, A174087.

Extensions

Name clarified and a(10)-a(15) from Bert Dobbelaere, May 19 2025