Past exam of the year 1 of the computer science course of the University of Oxford / 2015 / Functional programming, design and analysis of algorithms / 4 / b

Enumerate finite shells of constant coordinate sum:Here natural numbers include zero. Every generated coordinate is nonnegative. Conversely, a given triple $(a,b,c)$ occurs in exactly the shell $k=a+b+c$ and at exactly those loop indices $a,b$. Each shell contains only finitely many triples, so every triple is reached after finitely many earlier outputs. This is fair enumeration, unlike nesting three unrestricted infinite lists. For the positive-integer convention, add one to each generated coordinate.