Conway's LUX method for magic squares

Conway's LUX method for magic squares is an algorithm for creating magic squares of order 4n+2, where n is an integer.

Example square, of order 10, follows:

      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
 [1,]   68   65   96   93    4    1   32   29   60    57
 [2,]   66   67   94   95    2    3   30   31   58    59
 [3,]   92   89   20   17   28   25   56   53   64    61
 [4,]   90   91   18   19   26   27   54   55   62    63
 [5,]   16   13   24   21   49   52   80   77   88    85
 [6,]   14   15   22   23   50   51   78   79   86    87
 [7,]   37   40   45   48   76   73   81   84    9    12
 [8,]   38   39   46   47   74   75   82   83   10    11
 [9,]   41   44   69   72   97  100    5    8   33    36
[10,]   43   42   71   70   99   98    7    6   35    34