We consider approximation of N(n, E) and N c (n, E), the number of sequences of ASK symbols of length n with energy equal to E and at most equal to E, respectively. These quantities are often encountered in the context of constellation shaping, such as in shell mapping. We provide implementation techniques for our approximation methods. Numerical evaluation shows that approximations based on the techniques are extremely tight even at lengths as short as 16. Our presented approximation formulas for such quantities, theoretically justified, in conjunction with the implementation techniques, establish a new directional and theoretical foundation that can be applied to applications such as probabilistic shaping.