A055397 Maximum population of an n X n stable pattern in Conway's Game of Life.
0, 4, 6, 8, 16, 18, 28, 36, 43, 54, 64, 76, 90, 104, 119, 136, 152, 171, 190, 210, 232, 253, 276, 301, 326, 352, 379, 407, 437, 467, 497, 531, 563, 598, 633, 668, 706, 744, 782, 824, 864, 907, 949, 993, 1039, 1085, 1132, 1181, 1229, 1280, 1331, 1382, 1436
Offset: 1
Keywords
Examples
a(3) = 6 because a ship has 6 cells and no other 3 X 3 stable pattern has more.
Links
- G. Chu and P. J. Stuckey, A complete solution to the Maximum Density Still Life Problem, Artificial Intelligence, 184:1-16 (2012).
- G. Chu, K. E. Petrie, and N. Yorke-Smith, Constraint Programming to Solve Maximal Density Still Life, In Game of Life Cellular Automata chapter 10, A. Adamatzky, Springer-UK, 99-114 (2010).
- G. Chu, P. Stuckey, and M.G. de la Banda, Using relaxations in Maximum Density Still Life, In Proc. of Fifteenth Intl. Conf. on Principles and Practice of Constraint Programming, 258-273 (2009).
- Stephen Silver, Dense Stable Patterns
Formula
a(n) = (n^2)/2 + O(n).
For n >= 55, floor(n^2/2 + 17*n/27 - 2) <= a(n) <= ceiling(n^2/2 + 17*n/27 - 2), which gives all values of this sequence within +- 1.
Extensions
a(11)-a(27) from Nathaniel Johnston, May 15 2011, based on table in Chu et al.
a(28)-a(53) from Nathaniel Johnston, Nov 27 2013, based on work by Chu et al.