I would like to ask about the game Lights Out for a square nxn. In http://mathworld.wolfram.com/LightsOutPuzzle.html there is a list of the number of solutions to the game, and the number of solutions modulo symmetries of the square. Somewhere I have seen a formula for the number of solutions for general n, written as a generating function. However I cannot locate it now. Does anyone know where it is? And is there also a formula for the number of solutions modulo symmetries for general n? Thanks
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$\begingroup$ See also the earlier MO question, Randomly switching street lights, in a square city, concerning "Berlekamp’s Switching Game." $\endgroup$– Joseph O'RourkeCommented Feb 12, 2014 at 15:55
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1 Answer
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The number of solutions to the all-ones lights out problem on an $n\times n$ square, where nonidentical reflected and rotated solutions are considered distinct. (The link gives the Mathematica code to generate the sequence.)
Similarly, http://oeis.org/A075463 gives the number of rotation-reflection inequivalent solutions.
answered Feb 12, 2014 at 14:48
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$\begingroup$ My question is to find a closed formula (explicit formula or as a generating function) for these numbers, not just an algorithm to compute them one by one. $\endgroup$ Commented Feb 12, 2014 at 19:43
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1$\begingroup$ If there's no formula at the oeis pages, that's evidence that nobody has found one. But did you follow up on all the links at the oeis pages? $\endgroup$ Commented Feb 12, 2014 at 22:16