A261902 Irregular triangle read by rows: T(n,m) = number of permutations of {1, 2, ..., n} which form arithmetic progressions modulo m (n>=1, 1<=m<=n+2).

1, 1, 1, 2, 2, 2, 2, 6, 2, 6, 2, 2, 24, 8, 4, 8, 4, 2, 120, 12, 8, 4, 20, 2, 2, 720, 72, 48, 8, 8, 12, 6, 2, 5040, 144, 48, 16, 8, 4, 42, 4, 2, 40320, 1152, 144, 128, 16, 8, 12, 23, 6, 2, 362880, 2880, 1296, 96, 64, 16, 8, 8, 54, 4, 2

Offset

1,4

References

F. Luca, A. O. Munagi, The Number Of Permutations Which Form Arithmetic Progressions Modulo m, Annals of the Alexandru Ioan Cuza University, 2014, DOI: 10.2478/aicu-2014-0053

Links

Table of n, a(n) for n=1..63.

Example

Triangle begins:
1,1,1,
2,2,2,2,
6,2,6,2,2,
24,8,4,8,4,2,
120,12,8,4,20,2,2,
720,72,48,8,8,12,6,2,
5040,144,48,16,8,4,42,4,2,
40320,1152,144,128,16,8,12,23,6,2,
362880,2880,1296,96,64,16,8,8,54,4,2,
...

Crossrefs

T(n,n) = A002618(n).

Sequence in context: A130754 A164126 A343783 * A163368 A151948 A349923

Adjacent sequences: A261899 A261900 A261901 * A261903 A261904 A261905

Keyword

nonn,tabf

Author

N. J. A. Sloane, Sep 07 2015

Status

approved