

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.


2



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
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OFFSET

1,3


LINKS

Table of n, a(n) for n=1..46.
Sean A. Irvine, Illustration of Initial Terms of A059518, 2022.
Sean A. Irvine, Java program (github)


EXAMPLE

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.


CROSSREFS

Sequence in context: A294412 A227017 A073433 * A024929 A033816 A011889
Adjacent sequences: A059515 A059516 A059517 * A059519 A059520 A059521


KEYWORD

nonn,nice


AUTHOR

Zsolt Kukorelly (kukorell(AT)code.ucsd.edu), Feb 15 2001


EXTENSIONS

a(44) corrected by Sean A. Irvine, Oct 02 2022


STATUS

approved



