

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

Max Alekseyev and Thomas Buchholz, Table of n, a(n) for n = 1..1000. (Terms n=91 through n=1000 from Thomas Buchholz, May 20 2014)
M. Anderson and T. Feil, Turning Lights Out with Linear Algebra, Mathematics Magazine, 71 (1998), 300303.
Andries E. Brouwer, Lights Out and Button Madness Games. [Gives theory and a(n) for n = 1..1000, Jun 19 2008]
Eric Weisstein's World of Mathematics, Lights Out Puzzle


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

Cf. A159257.
Sequence in context: A078889 A176534 A154847 * A200604 A309038 A159468
Adjacent sequences: A165735 A165736 A165737 * A165739 A165740 A165741


KEYWORD

nonn


AUTHOR

Max Alekseyev, Sep 25 2009


EXTENSIONS

More terms from Thomas Buchholz, May 20 2014


STATUS

approved



