

A165738


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


3



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, 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, 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
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OFFSET

1,3


COMMENTS

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


REFERENCES

See A075462 for further references.


LINKS



FORMULA

a(n) <= 2n.
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


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



