[seqfan] Re: Duplicated "A*x+B" sequences

[Jaume Oliver i Lafont]

With regards to
http://list.seqfan.eu/pipermail/seqfan/2009-November/003082.html,
sequences with
a(n)=p*n+q-a(n-1)
also have
a(n-1)=p*(n-1)+q-a(n-2).

Subtracting these equations, the (simpler?) recurrence
a(n)=p+a(n-2)
is obtained.

Moreover, since
a(n-2)=p+a(n-4),
all of them satisfy the fourth-order linear recurrence
a(n)=2a(n-2)-a(n-4).

This is written as (0,2,0,-1) in the OEIS index for linear recurrences
http://research.att.com/~njas/sequences/Sindx_Rea.html#recLCC
, like sequences
http://research.att.com/~njas/sequences/A006370 and
http://research.att.com/~njas/sequences/A026741

The denominator in the g.f. for these family of sequences divides (1-x^2)^2.