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A006317 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)
0
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; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Does the density approach a limit?

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=1..23.

Jon Perry, kQueens

B. Recamán, Chess queens, Problem 89-8, Math. Intellig., 12 (No. 3, 1990), 65-68.

EXAMPLE

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

CROSSREFS

Sequence in context: A324125 A212293 A194102 * A194147 A077043 A022330

Adjacent sequences:  A006314 A006315 A006316 * A006318 A006319 A006320

KEYWORD

nonn,more

AUTHOR

N. J. A. Sloane

EXTENSIONS

a(9) from Jud McCranie, Jun 01 2003

a(10) >= 69. - Jud McCranie, Jun 08 2003

Edited by Jud McCranie, 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

STATUS

approved

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Last modified July 20 22:20 EDT 2019. Contains 325189 sequences. (Running on oeis4.)