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A063724 Consider problem of placing N queens on an n X n board so that each queen attacks precisely 4 others. Sequence gives maximal number of queens.

%I A063724 #16 Apr 01 2019 02:05:47
%S A063724 0,0,0,8,11,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66,69,
%T A063724 72,75,78,81,84,87,90,93,96,99,102,105,108,111,114,117,120,123,126,
%U A063724 129,132,135,138,141,144,147,150,153,156,159,162,165,168,171,174,177,180
%N A063724 Consider problem of placing N queens on an n X n board so that each queen attacks precisely 4 others. Sequence gives maximal number of queens.
%D A063724 Peter Hayes, A Problem of Chess Queens, Journal of Recreational Mathematics, 24(4), 1992, 264-271.
%F A063724 a(1)=a(2)=a(3)=0, a(4)=8, a(5)=11, a(n) = 3n - 3 for n >= 6.
%F A063724 From _Colin Barker_, Apr 13 2012: (Start)
%F A063724 a(n) = 2*a(n-1) - a(n-2) for n >= 8.
%F A063724 G.f.: x^4*(8 - 5*x + x^2 - x^3)/(1-x)^2. (End)
%e A063724 Examples from _Sean A. Irvine_, Mar 31 2019: (Start)
%e A063724 a(4) = 8:
%e A063724 .QQ.
%e A063724 Q..Q
%e A063724 Q..Q
%e A063724 .QQ.
%e A063724 a(5) = 11:
%e A063724 .Q.Q.
%e A063724 Q...Q
%e A063724 Q...Q
%e A063724 Q...Q
%e A063724 .QQQ.
%e A063724 a(6) = 15:
%e A063724 .Q..Q.
%e A063724 Q...QQ
%e A063724 Q.Q...
%e A063724 Q....Q
%e A063724 Q....Q
%e A063724 .QQQQ.
%e A063724 (End)
%Y A063724 Cf. A051754-A051759, A051567-A051571, A019654.
%K A063724 easy,nonn
%O A063724 1,4
%A A063724 _Jud McCranie_, Aug 11 2001