[seqfan] linear recurrence question

Kimberling, Clark ck6 at evansville.edu
Sun Apr 15 20:57:52 CEST 2012

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?


Clark Kimberling

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