Counting n-gons

[David Wilson]

And we should have a sequence that counts all simple integer-sided polygons 
of perimeter n. Depending on exactly what we are counting, the sequence 
might go:

a(3) = 1, the 1-1-1 triangle.
a(4) = 1, the 1-1-1-1 quadrilateral.
a(5) = 3, the 1-2-2 triangle, 1-1-1-2 quadrilateral, the 1-1-1-1-1 pentagon.

etc.