Contents: 1. Python file. Given the motional mode of an ion crystal calculates the mode-dependent coefficients (A,B-,C-,D-). Given the experimental parameters and sideband probability measurement, calculates the mean phonon number by solving the quartic equation derived in the paper. 2. Wolfram Mathematica notebook. Given the relevant Hamiltonian matrix elements calculates the explicit expressions for the crystal's ground state probabilities. By thermal averaging the ground state probabilities derives the full form of the equation connecting the sideband excitation probabilities with the mean phonon number.