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A055397 Maximum population of an n X n stable pattern in Conway's Game of Life. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
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.
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
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

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)