A076436 Square board sizes for which the lights-out problem has a unique solution (counting solutions differing only by rotation and reflection as distinct).

1, 2, 3, 6, 7, 8, 10, 12, 13, 15, 18, 20, 21, 22, 25, 26, 27, 28, 31, 36, 37, 38, 40, 42, 43, 45, 46, 48, 51, 52, 55, 56, 57, 58, 60, 63, 66, 68, 70, 72, 73, 75, 76, 78, 80, 81, 82, 85, 86, 87, 88, 90, 91, 93, 96, 97, 100, 102, 103, 105, 106, 108, 110, 111, 112, 115, 116, 117, 120

Offset: 1

Author

Eric W. Weisstein, Oct 11 2002

Keywords

• nonn

Comments

These are also the boards where any starting configuration can be turned off. - Robert Cowen (robert.cowen(AT)gmail.com), Jan 06 2007. [Comment corrected by Sune Kristian Jakobsen (sunejakobsen(AT)hotmail.com), Feb 04 2008]

Links

• N. J. A. Sloane and Thomas Buchholz, Table of n, a(n) for n = 1..1000 [terms were extended by N. J. A. Sloane (based on A117870), May 14 2006; terms 70 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

Crossrefs

Cf. A075462, A076437, A117872. Complement of A117870.

Formula

Positive integer n is in this sequence iff A159257(n)=0. [Max Alekseyev, Sep 25 2009]

Extensions

More terms from N. J. A. Sloane (based on A117870), May 14 2006, and Thomas Buchholz, May 16 2014