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).

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

Author

Maxim Karimov and Vladislav Sulima, Feb 03 2024

Keywords

• nonn
• tabl
• more

Comments

It is assumed that all beads lie on a circle and that the distance between any two adjacent beads is the same.

Examples

			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

Cf. A000012, A000027, A000290, A000578, A063776.

Formula

T(n,2) = A063776(n).