Editing Square triangular number (section)

==Recurrence relations==
The solution to the Pell equation can be expressed as a [[recurrence relation]] for the equation's solutions. This can be translated into recurrence equations that directly express the square triangular numbers, as well as the sides of the square and triangle involved.  We have<ref>{{MathWorld|title=Square Triangular Number|urlname=SquareTriangularNumber}}</ref>{{Rp|(12)}}

{{bi|left=1.6|<math>\displaystyle \begin{align}
N_k &= 34N_{k-1} - N_{k-2} + 2,& \text{with }N_0 &= 0\text{ and }N_1 = 1; \\
N_k &= \left(6\sqrt{N_{k-1}} - \sqrt{N_{k-2}}\right)^2,& \text{with }N_0 &= 0\text{ and }N_1 = 1.
\end{align}</math>}}

We have<ref name=Dickson /><ref name=Euler />{{Rp|13}}

{{bi|left=1.6|<math>\displaystyle \begin{align}
s_k &= 6s_{k-1} - s_{k-2},& \text{with }s_0 &= 0\text{ and }s_1 = 1; \\
t_k &= 6t_{k-1} - t_{k-2} + 2,& \text{with }t_0 &= 0\text{ and }t_1 = 1.
\end{align}</math>}}