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Number of ways to place n+1 queens and a pawn on an n X n board so that no two queens attack each other (symmetric solutions count only once).
2

%I #11 Dec 17 2023 03:15:58

%S 0,0,0,0,0,2,3,16,52,286,1403,8214,54756,389833,2923757,22932960,

%T 184339572

%N Number of ways to place n+1 queens and a pawn on an n X n board so that no two queens attack each other (symmetric solutions count only once).

%H R. D. Chatham, <a href="http://people.moreheadstate.edu/fs/d.chatham/n+kqueens.html">The N+k Queens Problem Page</a>.

%H R. D. Chatham, G. H. Fricke and R. D. Skaggs, <a href="http://people.moreheadstate.edu/fs/d.chatham/queenssep.pdf">The Queens Separation Problem</a>, Utilitas Mathematica 69 (2006), 129-141.

%H R. D. Chatham, M. Doyle, G. H. Fricke, J. Reitmann, R. D. Skaggs and M. Wolff, <a href="http://people.moreheadstate.edu/fs/d.chatham/QueensSep2.pdf">Indepe ndence and Domination Separation in Chessboard Graphs</a>, Journal of Combinatorial Mathematics and Combinatorial Computing, to appear.

%e For n=6 the a(6)=2 solutions are

%e . . Q . . . . . Q . . .

%e Q . P . . Q Q . P . . Q

%e . . . Q . . . . Q . . .

%e . Q . . . . . . . . Q .

%e . . . . Q . . Q . . . .

%e . . Q . . . . . . Q . .

%Y Cf. A103330, A002562, A368061.

%K more,nonn

%O 1,6

%A R. Douglas Chatham (d.chatham(AT)moreheadstate.edu), Jan 31 2005

%E More terms from R. Douglas Chatham (d.chatham(AT)moreheadstate.edu), Feb 15 2005, Apr 20 2007