|
%I #23 Nov 28 2019 06:14:57
%S 0,4,6,8,16,18,28,36,43,54,64,76,90,104,119,136,152,171,190,210,232,
%T 253,276,301,326,352,379,407,437,467,497,531,563,598,633,668,706,744,
%U 782,824,864,907,949,993,1039,1085,1132,1181,1229,1280,1331,1382,1436
%N Maximum population of an n X n stable pattern in Conway's Game of Life.
%H G. Chu and P. J. Stuckey, <a href="https://doi.org/10.1016/j.artint.2012.02.001">A complete solution to the Maximum Density Still Life Problem</a>, Artificial Intelligence, 184:1-16 (2012).
%H G. Chu, K. E. Petrie, and N. Yorke-Smith, <a href="https://doi.org/10.1007/978-1-84996-217-9_10">Constraint Programming to Solve Maximal Density Still Life</a>, In Game of Life Cellular Automata chapter 10, A. Adamatzky, Springer-UK, 99-114 (2010).
%H G. Chu, P. Stuckey, and M.G. de la Banda, <a href="https://doi.org/10.1007/978-3-642-04244-7_22">Using relaxations in Maximum Density Still Life</a>, In Proc. of Fifteenth Intl. Conf. on Principles and Practice of Constraint Programming, 258-273 (2009).
%H Stephen Silver, <a href="https://web.archive.org/web/20160712023902/http://www.argentum.freeserve.co.uk/dense.htm">Dense Stable Patterns</a>
%F a(n) = (n^2)/2 + O(n).
%F 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.
%e a(3) = 6 because a ship has 6 cells and no other 3 X 3 stable pattern has more.
%K nonn
%O 1,2
%A _Stephen A. Silver_, Jun 25 2000
%E a(11)-a(27) from _Nathaniel Johnston_, May 15 2011, based on table in Chu et al.
%E a(28)-a(53) from _Nathaniel Johnston_, Nov 27 2013, based on work by Chu et al.
|
