This site is supported by donations to The OEIS Foundation.

 Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A005311 Solution to Berlekamp's switching game (or lightbulb game) on an n X n board. (Formerly M1040) 1
 0, 1, 2, 4, 7, 11, 16, 22, 27, 35, 43, 54 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 REFERENCES Brown, Thomas A.; Spencer, Joel H. Minimization of +-1 - matrices under line shifts. Colloq. Math. 23 (1971), 165--171, 177 (errata insert). MR0307944 (46 #7059). Gives asymptotic bounds, some exact values, and generalizations to an m X n board. - N. J. A. Sloane, Jun 29 2014 Komlos, J., & Sulyok, M. (1970). On the sum of elements of +-1 matrices, in Combinatorial Theory and Its Applications (P. ErdÅ‘s et al., eds.), North-Holland, 721-728. Apparently gives exact solution on m X n board for m and n large. - N. J. A. Sloane, Jun 29 2014 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS 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!) N. J. A. Sloane, Solutions for 3 X 3 through 10x10 boards. Note that the so-called "solution" for n=10 is incorrect. N. J. A. Sloane, The box built by Elwyn Berlekamp in the 1960's. EXAMPLE 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 CROSSREFS Sequence in context: A002789 A083204 A061784 * A296202 A126613 A024224 Adjacent sequences:  A005308 A005309 A005310 * A005312 A005313 A005314 KEYWORD hard,nonn,more,nice AUTHOR EXTENSIONS Corrected and extended Dec 09 2003; last line of example corrected Dec 30 2004 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 16 17:02 EST 2018. Contains 318172 sequences. (Running on oeis4.)