A basis for the linear vector space consisting of polynomials in m,n, of deg\
    ree <=5

viewed as functions on the discrete lattice with the curious property that f\
    or every 1 by 4 discrete

rectangle in the plane, the value of the polynomial equals the average of it\
    s value at the other 9 locations is

                        2                2              2                 2
[1, -4 n + m, -4 n + 8 n  - 4 m n + 1/2 m  - 1/2 m, -2 m  n - 2 m n + 16 n

                      3        3        2                2         2
     - 22/3 n - 32/3 n  + 1/6 m  - 1/2 m  + 1/3 m + 8 m n , 112/3 n  - 82/5 n

           3         4        3                   2  2         2           3
     - 32 n  + 32/3 n  - 2/3 m  n - 20/3 m n + 4 m  n  + 12 m n  - 32/3 m n

             4        3   11  2                                   4   196
     + 1/24 m  - 1/4 m  + -- m  - 1/4 m, -184/5 n + 1/5 m - 1/12 m  - --- m n
                          24                                          15

       1424  2         2        2           2        3        2  2           3
     + ---- n  - 5/12 m  - 7/2 m  n + 32 m n  + 1/3 m  n + 4 m  n  - 80/3 m n
        15

               4         2  3        4          3  2          3         3
     + 32/3 m n  - 16/3 m  n  - 1/6 m  n + 4/3 m  n  - 272/3 n  + 7/24 m

              5   128  5          4
     + 1/120 m  - --- n  + 128/3 n ]
                  15

                          This took , 0.028, seconds