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

1,2

Links

Table of n, a(n) for n=1..53.

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.

Example

a(3) = 6 because a ship has 6 cells and no other 3 X 3 stable pattern has more.

Crossrefs

Sequence in context: A154387 A095299 A079250 * A239412 A295006 A269833

Adjacent sequences: A055394 A055395 A055396 * A055398 A055399 A055400

Keyword

nonn

Author

Stephen A. Silver, Jun 25 2000

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.

Status

approved