[seqfan] Re: linear recurrence multiples

[Fred Lunnon]

  I'm afraid it is unclear to me what is meant by "formula" in this context.
For example, does it mean "linear recurrence with integer coefficients,
such that at least one (or exactly one) coefficient equals  m " ?

  In that case the question would reduce to consideration of polynomial
multiples of a polynomial in a single variable.

WFL



On 7/19/19, Dale Gerdemann <dale.gerdemann at gmail.com> wrote:
> 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?
>
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