A |  0      1           2             3               4               n
                    -----------------------------------------------------------------------
                    0 |  1      2           3             4               5           n + 1
                    1 |  2      3           4             5               6           n + 2
                    2 |  3      5           7             9              11          2n + 3
                    3 |  5     13          29            61             125   2^(n + 3) - 3
                    4 | 13  65533  2^2^16 - 3  2^2^2^16 - 3  2^2^2^2^16 - 3  2^^(n + 3) - 3

It helps to use some new notation to indicate the value of A(4, n). Let 2^^n be a stack of 2's, n high. The top 2 of the stack is an exponent on the 2nd to top. 2^2 is an exponent on the 3rd to top, and so on. By the way, 2 + 2 = 2 * 2 = 2 ^ 2 = 2 ^^ 2.