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).

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

Offset

1,1

Comments

Numbers k such that a k X k 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]

Jaap's puzzle page, The Mathematics of Lights Out

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

Wikipedia, Lights Out (game)

Formula

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

Contains positive integers k such that A159257(k) > 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