Given a series of numbers how do I find the equation that describes the series?
For example given the following series of numbers...
$$352, 1424, 2528, 3664, 4832, 6032, 7264, 8528, 9824, 11152, 12512, 13904$$
The first differences are
$$1072, 1104, 1136, 1168, 1200, 1232, 1264, 1296, 1328, 1360, 1392$$ The second differences are all $32$
How can I find the function that describes this series.
Ultimately I am trying to determine which number in the series is a perfect square without doing trial division, There is a maximum of one perfect square in the series. My intention was to find the intersection of the set of perfect squares and the series above (and any other series that follows the same shape).
But before I worry about finding the intersection I am trying to understand how to convert a series of points into a function.
I hope that makes sense.