At (0,0) all the values of c are perfect squares (remainder e is always zero) and there is nothing to add to d to make the largest square. In other words in the cell at (0,0) we have all the squares with a square of size zero subtracted. It is the ONLY cell in row 0. No positive value of e has a cell in row zero.

In cell (0,1), e is zero, so all cs are perfect squares (the smaller square (x+n)(x+n) being 0). These values of c ALL appear in (0,0) but they also ALL have more than one way to arrange their factors. The factors this time produce an n value of 1. 4x4 = 16 can be arranged as 2x8 = 16, which is equal to 5x5 - 3x3. Notice that all the values of a in this cell are also each twice the value of a perfect square.

1+1 = 2

4+4 = 8

9+9 = 18

Notice that all the values of d for this cell also follow a pattern:

2x(1x2) = 4

2x(2x3) = 12

2x(3x4) = 24

All the values of d for (1,1) are identical to the values of a for (0,1). Notice also that all the values of a at (1,1) are the values of d in (0,1) with one added.

4+1 = 5

12+1 = 13

24+1 = 25

This cell (1,1) contains as values for a and b the values of two consecutive squares added together.

0+1 = 1

1+4 = 5

4+9 = 13

9+16 = 25

When two of these are multiplied together, the result is a twice a perfect square plus one as a remainder. Each value of a in cell (1,1) is also the long side of an integer right angled triangle.