How to calculate the total number of possible triangles where the perimeter is given, and all sides are integers? How would I go about calculating the total number of possible triangles where the perimeter is given, and all sides are integers?
Exempli gratia:


*

*$a + b + c = 15$

*$d + e + f = 16$

*$x + y + z = 100$


This is given in A005044.  The generating function is $\frac{x^3}{(1-x^2)(1-x^3)(1-x^4)}$  Some other formulas and references are given as well
