Generator for Almost Isosceles Pythagorean Triangle/Sequence

Sequence

The sequence of almost isosceles Pythagorean triangles 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 \\ 5 & 2 & 25 & 4 & 20 & 21 & 29 \\ 12 & 5 & 144 & 25 & 120 & 119 & 169 \\ 29 & 12 & 841 & 144 & 696 & 697 & 985 \\ 70 & 29 & 4900 & 841 & 4060 & 4059 & 5741 \\ 169 & 70 & 28 \, 561 & 4900 & 23 \, 660 & 23 \, 661 & 33 \, 461 \\ \hline \end{array}$

The sequence of elements of the generators are the Pell numbers:

$1, 2, 5, 12, 29, 70, 169, 408, \ldots$

This sequence is A000129 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Sources

• 1964: Albert H. Beiler: Recreations in the Theory of Numbers
• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $13$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $13$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $20$