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Search: id:A006317
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| A006317 |
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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.
(Formerly M2631)
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+0
1
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| 1, 3, 7, 12, 19, 27, 37, 46, 58, 71, 86, 102, 121, 137, 157, 178, 201, 225, 253, 276, 304, 334, 364
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Does the density approach a limit?
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
B. Recaman, Chess queens, Problem 89-8, Math. Intellig., 12 (No. 3, 1990), 65-68.
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LINKS
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Jon Perry, kQueens
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EXAMPLE
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Examples to illustrate a(10) and a(11) (1,2,3 are colors; 0 is an empty square):
1213121213
3002000302
2131302103
3020010321
2013230103
1320010201
2001323132
3132010201
2001030103
1323212321
and
12123212123
30001003001
21232321232
30010003001
12323212123
30010030001
21232121232
30010030010
12323212323
30010030010
21232121232
Examples to illustrate a(12)-a(14) (1,2,3 are colors; 0 is an empty square);
a(12) = 102:
121312131213
300203020302
213102010201
302031323132
201020010201
132313230103
201020102321
103010301003
321232123212
103010301030
201020102010
132313231323
a(13) = 121:
1232313121213
3001002003002
2123231312131
3001002003002
1232313121213
3001002003002
2123231312131
3001002003002
1232313121213
3001002003002
2123231312131
3001002003002
1232313121213
a(14) = 137:
12131212323132
30020030010201
21313121230103
30020030012321
12131212300103
30020030123201
21313120300102
30020031212301
12131200300102
30020312123231
21310003001002
30203121232313
20102003001002
13231312123231
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CROSSREFS
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Sequence in context: A008332 A065390 A062714 this_sequence A077043 A022330 A024219
Adjacent sequences: A006314 A006315 A006316 this_sequence A006318 A006319 A006320
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KEYWORD
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nonn,more
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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a(9) from Jud McCranie (j.mccranie(AT)comcast.net), Jun 01 2003
a(10) >= 69. - Jud McCranie (j.mccranie(AT)comcast.net), Jun 08 2003.
Edited by Jud McCranie (j.mccranie(AT)comcast.net), Jun 01, 2003
a(10) and a(11) from Tim Peters (tim.one(AT)comcast.net), Oct 15 2004, using a Python program.
a(12)-a(14) from Tim Peters (tim.one(AT)comcast.net), Nov 12 2004
a(15) - A(23) from Tim Peters (tim.one(AT)comcast.net), Oct 17 2006
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