A193452 Optimal towns for n>=1.

0, 1, 4, 8, 16, 25, 38, 54, 72, 96, 124, 152, 188, 227, 272, 318, 374, 433, 496, 563, 632, 716, 804, 895, 992, 1091, 1204, 1318, 1442, 1570, 1704, 1840, 1996, 2153, 2318, 2486, 2656, 2847, 3040, 3241, 3446, 3662, 3886, 4112, 4360, 4612, 4868, 5128, 5398

Offset

1,3

Comments

An n-town, n an integer, is a group of n buildings, each occupying a distinct position on a 2-dimensional integer grid. If we measure the distance between two buildings along the axis-parallel street grid, then an n-town 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.)

Links

Table of n, a(n) for n=1..49.

Erik D. Demaine, Sandor P. Fekete, Guenter Rote, Nils Schweer, Daria Schymura, Mariano Zelke, Integer Point Sets Minimizing Average Pairwise L1-Distance: What is the Optimal Shape of a Town?, arXiv:1009.5628 [cs.CG], 2010.

R. M. Karp, A. C. McKellar, C. K. Wong, Near-Optimal Solutions to a 2-Dimensional Placement Problem, SIAM J. Comput., 4(3), 271-286.

Crossrefs

Cf. A290190.

Sequence in context: A369566 A022560 A290190 * A003451 A277029 A013934

Adjacent sequences: A193449 A193450 A193451 * A193453 A193454 A193455

Keyword

nonn

Author

Ctibor O. Zizka, Jul 26 2011

Status

approved