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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.
2

%I #16 Apr 01 2019 02:05:47

%S 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 72,75,78,81,84,87,90,93,96,99,102,105,108,111,114,117,120,123,126,

%U 129,132,135,138,141,144,147,150,153,156,159,162,165,168,171,174,177,180

%N 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 Peter Hayes, A Problem of Chess Queens, Journal of Recreational Mathematics, 24(4), 1992, 264-271.

%F a(1)=a(2)=a(3)=0, a(4)=8, a(5)=11, a(n) = 3n - 3 for n >= 6.

%F From _Colin Barker_, Apr 13 2012: (Start)

%F a(n) = 2*a(n-1) - a(n-2) for n >= 8.

%F G.f.: x^4*(8 - 5*x + x^2 - x^3)/(1-x)^2. (End)

%e Examples from _Sean A. Irvine_, Mar 31 2019: (Start)

%e a(4) = 8:

%e .QQ.

%e Q..Q

%e Q..Q

%e .QQ.

%e a(5) = 11:

%e .Q.Q.

%e Q...Q

%e Q...Q

%e Q...Q

%e .QQQ.

%e a(6) = 15:

%e .Q..Q.

%e Q...QQ

%e Q.Q...

%e Q....Q

%e Q....Q

%e .QQQQ.

%e (End)

%Y Cf. A051754-A051759, A051567-A051571, A019654.

%K easy,nonn

%O 1,4

%A _Jud McCranie_, Aug 11 2001