[seqfan] linear recurrence question

[Kimberling, Clark]

Hello SeqFans,



Suppose that p,q,r,s are integers, and let a(n) be the number of triples (x,y,z) such that



p*x + q*y + r*z = s,



where x,y,z are all in {1,...,n}.  It appears that (a(n)) is a linear recurrence sequence -- and that x,y,z  can be replaced by x(1),x(2),...,x(k), etc.



Can someone provide a reference?



Thanks!



Clark Kimberling