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

4,1

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).

Links

Table of n, a(n) for n=4..15.

Example

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.

Sequence in context: A219423 A123213 A296822 * A193218 A220157 A264239

Adjacent sequences: A174081 A174082 A174083 * A174085 A174086 A174087

Keyword

nonn,more

Author

Isaac Lambert, Apr 20 2010

Extensions

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

Status

approved