# Lights out game

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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See also the earlier MO question, Randomly switching street lights, in a square city, concerning "Berlekamp’s Switching Game." –  Joseph O'Rourke Feb 12 '14 at 15:55

## 1 Answer

http://oeis.org/A075462

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.

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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. –  Vicente Munoz Feb 12 '14 at 19:43
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? –  Gerry Myerson Feb 12 '14 at 22:16