Here comes the main difference between Problem 140 and 137, after generating the first few terms the pattern is very difficult to find so instead we will solve the Pells equation: 5x^2 + 14x + 1 - y^2 = 0

Here is a great tool: Dario Alpern’s Generic Two integer variable equation solver

The tool generates the 2 recursive equations

(1) x_n+1 = - 9 ⁢x_n - 4 ⁢y_n - 14 ⁢

(2) y_n+1 = - 20 ⁢x_n - 9 ⁢y_n - 28 ⁢

With a bunch of starting values for x and y

From there you can code a simple recursion function much like the Fibonnaci sequence I showed in Problem 2 with all the different solutions