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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