[seqfan] Number of partitions of n into 4 nonzero squares

[Charles Greathouse]

I was looking at A025428 recently, and noticed that while new programs
have been added which are more efficient than the original, they still
take a long time to run* since they don't take advantage of any number
theory like Jacobi's theorem. Can anyone give an efficient formula
here? It should be more "tricky" than "hard", removing the
double-counting of negatives and taking out the 0s.

Actually my motivation was A216374, for which a formula has been
proposed which is presumably a special case of the yet-unwritten
formula for A025428.

* n^(1.5 + o(1)) when it should be n^o(1).

Charles Greathouse
Analyst/Programmer
Case Western Reserve University