Denote the respective length, breadth, width and the space diagonal of a rectangular cuboid as L, B, W and D.

Determine the total number of triplets (L, B, W) such that each of L,B,W and D is a positive integer with L+B+W = 29.

*** Order does not matter. For example (1,5,7) and (7,5,1) would be considered as different triplets.