%I
%S 0,1,4,8,16,25,38,54,72,96,124,152,188,227,272,318,374,433,496,563,
%T 632,716,804,895,992,1091,1204,1318,1442,1570,1704,1840,1996,2153,
%U 2318,2486,2656,2847,3040,3241,3446,3662,3886,4112,4360,4612,4868,5128,5398
%N Optimal towns for n>=1.
%C An ntown, n an integer, is a group of n buildings, each occupying a distinct position on a 2dimensional integer grid. If we measure the distance between two buildings along the axisparallel street grid, then an ntown has optimal shape if the sum of all pairwise Manhattan distances is minimized. (Data for this sequence are from Table 1, page 18, see reference link.)
%H Erik D. Demaine, Sandor P. Fekete, Guenter Rote, Nils Schweer, Daria Schymura, Mariano Zelke, <a href="http://arxiv.org/abs/1009.5628">Integer Point Sets Minimizing Average Pairwise L1Distance: What is the Optimal Shape of a Town?</a>, arXiv:1009.5628 [cs.CG], 2010.
%H R. M. Karp, A. C. McKellar, C. K. Wong, <a href="https://doi.org/10.1137/0204023">NearOptimal Solutions to a 2Dimensional Placement Problem,</a> SIAM J. Comput., 4(3), 271286.
%Y Cf. A290190.
%K nonn
%O 1,3
%A _Ctibor O. Zizka_, Jul 26 2011
