A059518 a(n)/n^2 is the minimal average squared Euclidean distance of n points to their center of gravity among all configurations of n points on the hexagonal lattice.
0, 1, 3, 8, 17, 29, 42, 69, 99, 135, 181, 228, 299, 371, 464, 560, 668, 788, 912, 1093, 1275, 1463, 1667, 1895, 2137, 2403, 2673, 2997, 3346, 3705, 4092, 4503, 4923, 5370, 5853, 6363, 6882, 7512, 8154, 8813, 9488, 10164, 10924, 11693, 12506, 13361
Offset: 1
Examples
a(2)=1 because the squared distance of (0,0) and of (1,0) to their center of gravity (1/2,0) is 1/4, resulting in an average of 1/4 = a(2)/2^2.
Links
- Sean A. Irvine, Illustration of Initial Terms of A059518, 2022.
- Sean A. Irvine, Java program (github)
Extensions
a(44) corrected by Sean A. Irvine, Oct 02 2022