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A117870 Square board sizes for which the lights-out problem does not have a unique solution (counting solutions differing only by rotation and reflection as distinct). 8
4, 5, 9, 11, 14, 16, 17, 19, 23, 24, 29, 30, 32, 33, 34, 35, 39, 41, 44, 47, 49, 50, 53, 54, 59, 61, 62, 64, 65, 67, 69, 71, 74, 77, 79, 83, 84, 89, 92, 94, 95, 98, 99, 101, 104, 107, 109, 113, 114, 118, 119, 123, 124, 125, 126, 128, 129, 131, 134, 135, 137, 139, 143 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers n such that an n X n parity pattern exists (see A118141). - Don Knuth, May 11 2006

LINKS

Max Alekseyev and Thomas Buchholz, Table of n, a(n) for n = 1..1000 [terms were extended by Max Alekseyev, Sep 17 2009; terms 64 through 1000 were computed by Thomas Buchholz, May 16 2014]

K. Sutner, Linear cellular automata and the Garden-of-Eden, Math. Intelligencer, 11 (No. 2, 1989), 49-53.

Eric Weisstein's World of Mathematics, Lights-Out Puzzle

The Mathematics of Lights Out (on Jaap's puzzle page)

Wikipedia, Lights Out (game)

FORMULA

a(n) = A093614(n) - 1.

Contains positive integers n such that A159257(n)>0. - Max Alekseyev, Sep 17 2009

CROSSREFS

Cf. A075462, A076437, A117872. Complement of A076436.

Sequence in context: A224862 A010416 A134921 * A162698 A166562 A031363

Adjacent sequences:  A117867 A117868 A117869 * A117871 A117872 A117873

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, May 14 2006

EXTENSIONS

More terms from Max Alekseyev, Sep 17 2009, and Thomas Buchholz, May 16 2014

STATUS

approved

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Last modified August 10 08:28 EDT 2020. Contains 336368 sequences. (Running on oeis4.)