%I M2631 #23 Mar 30 2014 04:18:01
%S 1,3,7,12,19,27,37,46,58,71,86,102,121,137,157,178,201,225,253,276,
%T 304,334,364
%N Maximum number of chess queens of 3 colors on an n X n board such that no queen attacks or protects another queen of its color.
%C Does the density approach a limit?
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Jon Perry, <a href="http://www.users.globalnet.co.uk/~perry/maths/kQueens/kQueens.htm">kQueens</a>
%H B. Recamán, <a href="http://dx.doi.org/10.1007/BF03024021">Chess queens, Problem 89-8</a>, Math. Intellig., 12 (No. 3, 1990), 65-68.
%e Examples to illustrate a(10) and a(11) (1,2,3 are colors; 0 is an empty square):
%e 1213121213
%e 3002000302
%e 2131302103
%e 3020010321
%e 2013230103
%e 1320010201
%e 2001323132
%e 3132010201
%e 2001030103
%e 1323212321
%e and
%e 12123212123
%e 30001003001
%e 21232321232
%e 30010003001
%e 12323212123
%e 30010030001
%e 21232121232
%e 30010030010
%e 12323212323
%e 30010030010
%e 21232121232
%e Examples to illustrate a(12)-a(14) (1,2,3 are colors; 0 is an empty square);
%e a(12) = 102:
%e 121312131213
%e 300203020302
%e 213102010201
%e 302031323132
%e 201020010201
%e 132313230103
%e 201020102321
%e 103010301003
%e 321232123212
%e 103010301030
%e 201020102010
%e 132313231323
%e a(13) = 121:
%e 1232313121213
%e 3001002003002
%e 2123231312131
%e 3001002003002
%e 1232313121213
%e 3001002003002
%e 2123231312131
%e 3001002003002
%e 1232313121213
%e 3001002003002
%e 2123231312131
%e 3001002003002
%e 1232313121213
%e a(14) = 137:
%e 12131212323132
%e 30020030010201
%e 21313121230103
%e 30020030012321
%e 12131212300103
%e 30020030123201
%e 21313120300102
%e 30020031212301
%e 12131200300102
%e 30020312123231
%e 21310003001002
%e 30203121232313
%e 20102003001002
%e 13231312123231
%K nonn,more
%O 1,2
%A _N. J. A. Sloane_
%E a(9) from _Jud McCranie_, Jun 01 2003
%E a(10) >= 69. - _Jud McCranie_, Jun 08 2003
%E Edited by _Jud McCranie_, Jun 01 2003
%E a(10) and a(11) from Tim Peters (tim.one(AT)comcast.net), Oct 15 2004, using a Python program
%E a(12)-a(14) from Tim Peters (tim.one(AT)comcast.net), Nov 12 2004
%E a(15)-a(23) from Tim Peters (tim.one(AT)comcast.net), Oct 17 2006