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A055397
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Maximum population of an n X n stable pattern in Conway's Game of Life.
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2
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| All terms of this sequence are known within +/- 1. The first term that is unknown is a(28), which is either 406 or 407. The values of a(29)-a(37) are 437, 466, 497, 530, 563, 598, 632, 668, and 706. - Nathaniel Johnston, May 15 2011
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REFERENCES
| G. Chu, K. E. Petrie, 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, 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).
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LINKS
| Stephen Silver, Dense Stable Patterns
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FORMULA
| a(n) = (n^2)/2 + O(n).
For n>=55, floor(n^2/2 + 17*n/27 - 2) <= a(n) <= ceil(n^2/2 + 17*n/27 - 2), which gives all values of this sequence within +/- 1.
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EXAMPLE
| a(3) = 6 because a ship has 6 cells and no other 3 X 3 stable pattern has more.
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CROSSREFS
| Sequence in context: A154387 A095299 A079250 * A049421 A039624 A083166
Adjacent sequences: A055394 A055395 A055396 * A055398 A055399 A055400
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KEYWORD
| nonn
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AUTHOR
| Stephen A. Silver (maths(AT)argentum.freeserve.co.uk), Jun 25 2000
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EXTENSIONS
| a(11) - a(27) from Nathaniel Johnston (nathaniel(AT)nathanieljohnston.com), May 15 2011, based on table in Chu et. al.
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