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%I #32 Feb 12 2024 06:34:43
%S 4,6,8,10,12,16,18,20,22,24,28,30,32,34,36,40,42,44,46,48,52,54,56,58,
%T 60,64,66,68,70,72,76,78,80,82,84,88,90,92,94,96,100,102,104,106,108,
%U 112,114,116,118,120,124,126,128,130,132,136,138,140,142,144
%N Consider the problem of placing N queens on an n X n board so that each queen attacks precisely 3 others. Sequence gives maximal number of queens.
%C a(n) <= 2[(6n-2)/5]. - _Jud McCranie_, Aug 12 2001
%C Conjecture: a(n) = 2[(6n-2)/5] for n >= 2; verified up to n = 100. - _Alexander D. Healy_, Feb 11 2024
%D Martin Gardner, The Last Recreations, Copernicus, NY, 1997, 274-283.
%D Peter Hayes, A Problem of Chess Queens, Journal of Recreational Mathematics, Baywood, 24(4), 1992, 264-271.
%H Alexander D. Healy, <a href="/A051756/a051756_1.pdf">Examples of optimal placements for n <= 61</a>
%e Examples from _R. J. Mathar_, May 01 2006: (Start)
%e ==== n = 3
%e 6 queens:
%e Q Q Q
%e Q - -
%e Q - Q
%e 6 queens:
%e Q Q Q
%e - - -
%e Q Q Q
%e ==== n = 4
%e 8 queens:
%e Q Q Q Q
%e Q - - -
%e Q - - -
%e Q - - Q
%e 8 queens:
%e Q Q Q Q
%e Q - - -
%e - - Q -
%e Q - - Q
%e 8 queens:
%e Q Q Q Q
%e - - - -
%e - - - -
%e Q Q Q Q
%e 8 queens:
%e Q Q - Q
%e - Q - -
%e - - Q -
%e Q - Q Q
%e ==== n = 7
%e 16 queens:
%e Q Q Q - Q - Q
%e - - - - - - Q
%e - - - Q - - -
%e Q - - - - - Q
%e - - - Q - - -
%e Q - - - - - -
%e Q - Q - Q Q Q
%e 16 queens:
%e Q Q Q - - Q Q
%e - - - Q - - -
%e - - - - - - Q
%e Q - - - - - Q
%e Q - - - - - -
%e - - - Q - - -
%e Q Q - - Q Q Q
%e (End)
%Y Cf. A051754, A051755, A051757, A051758, A051759, A051567, A051568, A051569, A051570, A051571, A019654.
%K nonn,nice
%O 2,1
%A Robert Trent (trentrd(AT)hotmail.com), Aug 23 2000
%E More terms from _Jud McCranie_, Aug 12 2001
%E a(10)-a(61) from _Alexander D. Healy_, Feb 11 2024
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