Pythagorean Triangle whose Hypotenuse and Leg differ by 1/Sequence

Sequence
The sequence of Pythagorean triangles whose hypotenuse and leg differ by 1 can be tabulated as follows:


 * $\begin{array} {r r | r r | r r r}

m & n & m^2 & n^2 & 2 m n & m^2 - n^2 & m^2 + n^2 \\ \hline 2 & 1 & 4 & 1 & 4 & 3 & 5 \\ 3 & 2 & 9 & 4 & 12 & 5 & 13 \\ 4 & 3 & 16 & 9 & 24 & 7 & 25 \\ 5 & 4 & 25 & 16 & 40 & 9 & 41 \\ 6 & 5 & 36 & 25 & 60 & 11 & 61 \\ 7 & 6 & 49 & 36 & 84 & 13 & 85 \\ \hline \end{array}$