Problem with Queens and Pawns

[Erich Friedman]

>Consider an n X n chessboard. Place n queens in the cells of the first row,
>namely in the cells (1,1), (2,1),..., (n,1), and [(n+1)/2] pawns in the
>odd cells of the second row, namely in the cells (1,2), (3,2), (5,2), ...
>Which is the number of the unattacked (by the queens) cells ?
>n |  1 2 3 4 5 6  7  8  9 10 11 12 13 14 15 .....
>__|______________________________________________
># |  0 0 0 2 4 7 10 14 19 24 30 36 44 51 60 .....
>Formula ??

look at only the even index terms, and compute second differences:

0   2   7  14  24  36  51
  2   5   7  10  12  15
    3   2   3   2   3

the same thing happens when we do only the odd index terms:

0   4  10  19  30  44  60
  4   6   9  11  14  16
    2   3   2   3   2

hope this helps.

erich friedman
http://www.stetson.edu/~efriedma