[seqfan] linear recurrence multiples

[Dale Gerdemann]

I have a question concerning recurrences of the form a(0)=0, a(1)=1,a(n) =
b*a(n-1)+c*a(n-2). When (b,c) is (3,2), for example, we have A007482 and
when (b,c)=(2,3), we have A015518. For A007482, it seems to be possible to
find formulae for m*a(n) for any m. For example, if m=4, we have 4*a(n) =
a(n+1)+a(n-1)+2*a(n-2). For A015518,  however, it seems that no such
formulae can be found. It appears that such formulae can be found just in
case b >= c. Is this correct?