cp's OEIS Frontend

A370108 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 can be transformed by rotation into the convex hull of a set of beads of any other color B (n >= 1, k >= 1).

%I A370108 #53 Mar 25 2024 06:45:56
%S A370108 0,0,0,0,1,0,0,3,0,0,0,6,2,2,0,0,10,8,6,0,0,0,15,20,18,0,2,0,0,21,40,
%T A370108 50,0,10,0,0,0,28,70,120,24,28,0,4,0,0,36,112,252,144,60,0,12,0,0,0,
%U A370108 45,168,476,504,230,0,54,8,4,0
%N A370108 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 can be transformed by rotation into the convex hull of a set of beads of any other color B (n >= 1, k >= 1).
%C A370108 It is assumed that all beads lie on a circle and distance between any two adjacent is the same.
%F A370108 T(n,2) = A000013(ceiling(n/2)) * [n mod 2 == 0], where [] is the Iverson bracket.
%F A370108 For prime p, T(p,k) = (p-1)! * binomial(k,p).
%e A370108 n\k| 1 2  3  4   5   6    7    8     9 ...
%e A370108 ---+----------------------------------
%e A370108  1 | 0 0  0  0   0   0    0    0     0 ... A000007
%e A370108  2 | 0 1  3  6  10  15   21   28    36 ... A000217
%e A370108  3 | 0 0  2  8  20  40   70  112   168 ... A007290
%e A370108  4 | 0 2  6 18  50 120  252  476   828 ... A062026
%e A370108  5 | 0 0  0  0  24 144  504 1344  3024 ... A059593
%e A370108  6 | 0 2 10 28  60 230 1022 3640 10488
%e A370108  7 | 0 0  0  0   0   0  720 5760 25920 ... A153760
%e A370108  8 | 0 4 12 54 190 510 1134 7252 49284
%e A370108  9 | 0 0  8 32  80 160  280  448 40992
%e A370108 ...
%Y A370108 Cf. A000007, A000013, A000217, A007290, A062026, A059593, A153760.
%K A370108 nonn,tabl,more
%O A370108 1,8
%A A370108 _Maxim Karimov_ and Vladislav Sulima, Feb 10 2024