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A165738 Rank deficiency (= dimension of the null space) of the n X n "Lights Out" puzzle on a torus. 3


%S 0,0,4,0,8,8,0,0,4,16,0,16,0,0,12,0,16,8,0,32,4,0,0,32,8,0,4,0,0,24,

%T 40,0,44,32,8,16,0,0,4,64,0,8,0,0,12,0,0,64,0,16,20,0,0,8,8,0,4,0,0,

%U 48,0,80,52,0,56,88,0,64,4,16,0,32,0,0,12,0,0,8,0,128,4,0,0,16,24,0,4,0,0,24

%N Rank deficiency (= dimension of the null space) of the n X n "Lights Out" puzzle on a torus.

%C The number of solutions to the puzzle is 2^a(n). If a(n)=0 then the puzzle has a unique solution.

%D See A075462 for further references.

%H Max Alekseyev and Thomas Buchholz, <a href="/A165738/b165738.txt">Table of n, a(n) for n = 1..1000</a>. (Terms n=91 through n=1000 from Thomas Buchholz, May 20 2014)

%H M. Anderson and T. Feil, <a href="http://www.jstor.org/stable/2690705">Turning Lights Out with Linear Algebra</a>, Mathematics Magazine, 71 (1998), 300-303.

%H Andries E. Brouwer, <a href="http://www.win.tue.nl/~aeb/ca/madness/madrect.html">Lights Out and Button Madness Games</a>. [Gives theory and a(n) for n = 1..1000, Jun 19 2008]

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LightsOutPuzzle.html">Lights Out Puzzle</a>

%F a(n) <= 2n.

%F a(n) is a multiple of 4 and satisfies a(2n) = 2a(n). a(n+1) = 2 * A159257(n) + 4 if n = 2 (mod 3) and a(n+1) = 2 * A159257(n) otherwise. - _Thomas Buchholz_, May 22 2014

%Y Cf. A159257.

%K nonn

%O 1,3

%A _Max Alekseyev_, Sep 25 2009

%E More terms from _Thomas Buchholz_, May 20 2014

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Last modified January 26 20:11 EST 2020. Contains 331288 sequences. (Running on oeis4.)