http://list.seqfan.eu/pipermail/seqfan/2009-November/003088.html Richard, Yes, thank you, order three is enough. I should have combined a(n)=p+a(n-2) with a(n-1)=p+a(n-3) to get a(n)=a(n-1)+a(n-2)-a(n-3) A case with order even smaller than three: a(n)=2n+1-a(n-1) with a(0)=1 is a(n)=n+1, with g.f. 1/(1-x)^2. Jaume