cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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.

Original entry on oeis.org

21, 94, 544, 3509, 26799, 223123, 2133511, 21793042, 248348572, 3008632130, 39989075942, 558800689295
Offset: 4

Views

Author

Isaac Lambert, Apr 20 2010

Keywords

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

Extensions

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

A174086 Number of permutations of length n with no consecutive triples i,...i+r,...i+2r (mod n) for all r, and for all equal spacings d.

Original entry on oeis.org

16, 40, 204, 840, 6272, 35856, 378000, 2638460, 28387728, 249444936, 3275745564, 30770034480
Offset: 4

Views

Author

Isaac Lambert, Apr 20 2010

Keywords

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 note a(4) is the same as the value in A165963 since there are no other distances that can be used (i.e. only d=1).
		

Crossrefs

Extensions

a(10)-a(15) from Bert Dobbelaere, May 18 2025

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

Original entry on oeis.org

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

Views

Author

Isaac Lambert, Apr 20 2010

Keywords

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.
		

Crossrefs

Showing 1-3 of 3 results.