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Search: id:A005311
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| A005311 |
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Solution to Berlekamp's switching game on n X n board.
(Formerly M1040)
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+0
1
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| 0, 1, 2, 4, 7, 11, 16, 22, 27, 35, 43, 54
(list; graph; listen)
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OFFSET
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1,3
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
J. Carlson and D. Stolarski, The correct solution to Berlekamp's switching game, Discrete Math., Vol. 287 (2004).
P. C. Fishburn and N. J. A. Sloane, The solution to Berlekamp's switching game, Discrete Math., 74 (1989), 263-290. (Apparently our value a(10) = 34 is incorrect!)
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LINKS
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N. J. A. Sloane, Solutions for 3 X 3 through 10x10 boards.
N. J. A. Sloane, The box built by Elwyn Berlekamp in the 1960's.
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EXAMPLE
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According to Calson and Stolarski, the following position with 35 lights on cannot be reduced:
xxx00xx000
xx0xx000x0
0xxx00000x
x0x0x00x00
x00x0x0x00
0x00xx0000
000xx0x000
0x0000xx00
000x0000x0
x00000000x
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CROSSREFS
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Sequence in context: A024673 A083204 A061784 this_sequence A126613 A024224 A025727
Adjacent sequences: A005308 A005309 A005310 this_sequence A005312 A005313 A005314
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KEYWORD
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hard,nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Corrected and extended, Dec 09, 2003. The last line of the example was corrected Dec 30 2004.
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