[seqfan] Re: linear recurrence question
Max Alekseyev
maxale at gmail.com
Mon Apr 16 20:04:23 CEST 2012
Constrains p*x + q*y + r*z = s, 1 <= x,y,z <= n define a 2-d polygon
in 3-d space.
So a(n) may be even a polynomial in n -- see
http://en.wikipedia.org/wiki/Ehrhart_polynomial
Max
On Sun, Apr 15, 2012 at 2:57 PM, Kimberling, Clark <ck6 at evansville.edu> wrote:
> Hello SeqFans,
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> Suppose that p,q,r,s are integers, and let a(n) be the number of triples (x,y,z) such that
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> p*x + q*y + r*z = s,
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> 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.
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> Can someone provide a reference?
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> Thanks!
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> Clark Kimberling
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