Representation numbers of certain quaternary quadratic forms in a genus consisting of a single class (Q2816454)

The well-known Nipp's tables of quaternary quadratic forms provide 75 reduced positive definite quaternary quadratic forms with discriminant \(\leq 1732\) that are sums of two binary quadratic forms, and belong to a genus containing one and only one forms class. The goal is to determinate an explicit formulas for the representation numbers of integers by such forms. For 27 diagonal and 24 non-diagonal forms from the considered list, these formulas can be found in the literature. NEWLINENEWLINENEWLINEThe authors prove the required formulas for the remaining 24 non-diagonal forms.