Sequences of experimental ground-state energies for both odd and even A are mapped onto concave patterns cured from convexities due to pairing. These patterns yield improved estimates by interpolation or extrapolation (as appropriate) of ground-state energies for nuclei, which have not yet been measured. An example of this procedure, using the tin isotopes is given. The same patterns, completed by a list of excitation energies, give numerical estimates of thermodynamical functions, which lead to the average nucleon number (A) (β,μ) becoming a continuous variable at low to moderate temperatures, allowing extrapolations towards nuclear masses closer to drip lines. Estimates of the free energy and the average energy, as functions of (A), provide upper and lower bounds, respectively, to ground-state energy. Finally, we discuss extensions to a two-dimensional analysis and how concavity and universality are related to the theory of the nuclear density functional.