How would I find the equation to calculate the 4th value based off of the first 3

Treat index,value as coordinates in a 2D space. So your 3 values become 3 points on a plane. Those 3 points happen to lie on a line, so find the equation for that line, and you can find all the other points on the line.

Usually in mathematics (and computer science), we start sequences with the 0th element, so the 3 points you get are

0, 93222358
1, 131836323
2, 170450288

which are in a line. If they were not on a line, you could still solve for a 2nd degree polynomial that fits the 3 points, and use that to derive additional values. In general, given N values, you can find a degree N-1 polynomial that will give you further values in the sequence.