Pythagorean Triples in Disguise?

There are \(n\) nonnegative integral solutions to the equation

\[(x^2-y^2)^2=16y+1\]

obviously all in the form \((x_1, y_1), (x_2, y_2),\dots,(x_n, y_n)\). Compute

\[\sum_{a=1}^{n}x_a+y_a\]

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