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A369878
Array read by antidiagonals: T(n,k) is the number of length n necklaces using at most k colors in which the convex hull of a set of beads of any color A cannot be transformed by rotation into the convex hull of a set of beads of any other color B (n >= 1, k >= 1).
0
1, 2, 1, 3, 2, 1, 4, 3, 4, 1, 5, 4, 9, 4, 1, 6, 5, 16, 9, 8, 1, 7, 6, 25, 16, 27, 12, 1, 8, 7, 36, 25, 64, 93, 20, 1, 9, 8, 49, 36, 125, 304, 243, 32, 1, 10, 9, 64, 49, 216, 705, 928, 699, 60, 1, 11, 10, 81, 64, 343, 1356, 2405, 4384, 2019, 104, 1
OFFSET
1,2
COMMENTS
It is assumed that all beads lie on a circle and that the distance between any two adjacent beads is the same.
FORMULA
T(n,2) = A063776(n).
EXAMPLE
n\k| 1 2 3 4 5 6 7 8 9 ...
---+---------------------------------------------------
1 | 1 2 3 4 5 6 7 8 9 ... A000027
2 | 1 2 3 4 5 6 7 8 9 ... A000027
3 | 1 4 9 16 25 36 49 64 81 ... A000290
4 | 1 4 9 16 25 36 49 64 81 ... A000290
5 | 1 8 27 64 125 216 343 512 729 ... A000578
6 | 1 12 93 304 705 1356 2317 3648 5409
7 | 1 20 243 928 2405 5076 9415 15968 25353
8 | 1 32 699 4384 15245 39216 84007 159104 275769
9 | 1 60 2019 18256 72765 202236 457135 902784 1620441
...
CROSSREFS
KEYWORD
nonn,tabl,more
AUTHOR
Maxim Karimov and Vladislav Sulima, Feb 03 2024
STATUS
approved