A103330 -id:A103330 - cp's OEIS frontend

A103331 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).

0, 0, 0, 0, 0, 2, 3, 16, 52, 286, 1403, 8214, 54756, 389833, 2923757, 22932960, 184339572

Offset: 1

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

			For n=6 the a(6)=2 solutions are
 . . Q . . .    . . Q . . .
 Q . P . . Q    Q . P . . Q
 . . . Q . .    . . Q . . .
 . Q . . . .    . . . . Q .
 . . . . Q .    . Q . . . .
 . . Q . . .    . . . Q . .

R. D. Chatham, The N+k Queens Problem Page.
R. D. Chatham, G. H. Fricke and R. D. Skaggs, The Queens Separation Problem, Utilitas Mathematica 69 (2006), 129-141.
R. D. Chatham, M. Doyle, G. H. Fricke, J. Reitmann, R. D. Skaggs and M. Wolff, Indepe ndence and Domination Separation in Chessboard Graphs, Journal of Combinatorial Mathematics and Combinatorial Computing, to appear.

Cf. A103330, A002562, A368061.

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

A368061 The number of ways to place one pawn and n+1 nonattacking queens on an n X n chessboard, unchanged by 180-degree rotation.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 0, 5, 0, 18, 0, 50, 0, 652, 0, 4260, 0, 25134, 0, 238098, 0, 2492304, 0, 25389294

Offset: 1

Don Knuth, Dec 10 2023

n must be odd, and the pawn must be in the center.

			For n=7 the a(7)=1 solution is
  . . Q . . . .
  . . . . . Q .
  . . . Q . . .
  Q . . P . . Q
  . . . Q . . .
  . Q . . . . .
  . . . . Q . .

A103330 counts all solutions; A103331 counts them with symmetry removed.

A103330(n) = 8*A103331(n) - 4*a(n).

cp's OEIS Frontend

A103331 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).

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