OFFSET
1,8
COMMENTS
It is assumed that all beads lie on a circle and distance between any two adjacent is the same.
FORMULA
T(n,2) = A000013(ceiling(n/2)) * [n mod 2 == 0], where [] is the Iverson bracket.
For prime p, T(p,k) = (p-1)! * binomial(k,p).
EXAMPLE
n\k| 1 2 3 4 5 6 7 8 9 ...
---+----------------------------------
1 | 0 0 0 0 0 0 0 0 0 ... A000007
2 | 0 1 3 6 10 15 21 28 36 ... A000217
3 | 0 0 2 8 20 40 70 112 168 ... A007290
4 | 0 2 6 18 50 120 252 476 828 ... A062026
5 | 0 0 0 0 24 144 504 1344 3024 ... A059593
6 | 0 2 10 28 60 230 1022 3640 10488
7 | 0 0 0 0 0 0 720 5760 25920 ... A153760
8 | 0 4 12 54 190 510 1134 7252 49284
9 | 0 0 8 32 80 160 280 448 40992
...
CROSSREFS
KEYWORD
AUTHOR
Maxim Karimov and Vladislav Sulima, Feb 10 2024
STATUS
approved