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
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
Similarly, http://oeis.org/A075463 gives the number of rotation-reflection inequivalent solutions.