A294240 - OEIS

A294240

The number of possible ways in which 2*n^2 black pawns and 2*n^2 white pawns can be arranged on a 2n X 2n chessboard such that no pawn attacks another.

%I #19 Aug 13 2022 20:49:42

%S 1,3,30,410,6148,96120,1526700,24425026,392143828,6306613690,

%T 101505099104,1634209596410,26311180850268,423567557239604,

%U 6817440328754244,109703307312544664,1764863031686159684,28385338557467333804,456426743658724223028,7337464027218416593362

%N The number of possible ways in which 2*n^2 black pawns and 2*n^2 white pawns can be arranged on a 2n X 2n chessboard such that no pawn attacks another.

%C White pawns attack diagonally up and black pawns attack diagonally down.

%C En passant capturing is not possible.

%H Code Golf Stack Exchange user feersum, <a href="https://codegolf.stackexchange.com/a/52224/53884">Too many pawns on a chess board</a>.

%e For n = 1 the a(1) = 3 boards are as follows:

%e +---+---+ +---+---+ +---+---+

%e | W | W | | B | W | | W | B |

%e +---+---+ +---+---+ +---+---+

%e | B | B | | W | B | | B | W |

%e +---+---+ +---+---+ +---+---+

%e .

%e An example of one of the a(2) = 30 boards is:

%e +---+---+---+---+

%e | W | W | W | W |

%e +---+---+---+---+

%e | B | W | W | W |

%e +---+---+---+---+

%e | B | B | W | B |

%e +---+---+---+---+

%e | B | B | B | B |

%e +---+---+---+---+

%Y Cf. A035290.

%K nonn

%O 0,2

%A _Peter Kagey_, Oct 25 2017