A117870 - OEIS

%I #25 Jan 03 2022 03:01:04

%S 4,5,9,11,14,16,17,19,23,24,29,30,32,33,34,35,39,41,44,47,49,50,53,54,

%T 59,61,62,64,65,67,69,71,74,77,79,83,84,89,92,94,95,98,99,101,104,107,

%U 109,113,114,118,119,123,124,125,126,128,129,131,134,135,137,139,143

%N 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).

%C Numbers k such that a k X k parity pattern exists (see A118141). - _Don Knuth_, May 11 2006

%H Max Alekseyev and Thomas Buchholz, <a href="/A117870/b117870.txt">Table of n, a(n) for n = 1..1000</a> [terms were extended by Max Alekseyev, Sep 17 2009; terms 64 through 1000 were computed by Thomas Buchholz, May 16 2014]

%H Jaap's puzzle page, <a href="http://www.jaapsch.net/puzzles/lomath.htm">The Mathematics of Lights Out</a>

%H K. Sutner, <a href="http://dx.doi.org/10.1007/BF03023823">Linear cellular automata and the Garden-of-Eden</a>, Math. Intelligencer, 11 (No. 2, 1989), 49-53.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LightsOutPuzzle.html">Lights-Out Puzzle</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Lights_Out_(game)">Lights Out (game)</a>

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

%F Contains positive integers k such that A159257(k) > 0. - _Max Alekseyev_, Sep 17 2009

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

%K nonn

%O 1,1

%A _N. J. A. Sloane_, May 14 2006

%E More terms from _Max Alekseyev_, Sep 17 2009, and _Thomas Buchholz_, May 16 2014