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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 A294240 #19 Aug 13 2022 20:49:42
%S A294240 1,3,30,410,6148,96120,1526700,24425026,392143828,6306613690,
%T A294240 101505099104,1634209596410,26311180850268,423567557239604,
%U A294240 6817440328754244,109703307312544664,1764863031686159684,28385338557467333804,456426743658724223028,7337464027218416593362
%N 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.
%C A294240 White pawns attack diagonally up and black pawns attack diagonally down.
%C A294240 En passant capturing is not possible.
%H A294240 Code Golf Stack Exchange user feersum, <a href="https://codegolf.stackexchange.com/a/52224/53884">Too many pawns on a chess board</a>.
%e A294240 For n = 1 the a(1) = 3 boards are as follows:
%e A294240   +---+---+    +---+---+    +---+---+
%e A294240   | W | W |    | B | W |    | W | B |
%e A294240   +---+---+    +---+---+    +---+---+
%e A294240   | B | B |    | W | B |    | B | W |
%e A294240   +---+---+    +---+---+    +---+---+
%e A294240 .
%e A294240 An example of one of the a(2) = 30 boards is:
%e A294240   +---+---+---+---+
%e A294240   | W | W | W | W |
%e A294240   +---+---+---+---+
%e A294240   | B | W | W | W |
%e A294240   +---+---+---+---+
%e A294240   | B | B | W | B |
%e A294240   +---+---+---+---+
%e A294240   | B | B | B | B |
%e A294240   +---+---+---+---+
%Y A294240 Cf. A035290.
%K A294240 nonn
%O A294240 0,2
%A A294240 _Peter Kagey_, Oct 25 2017