[seqfan] Re: A089068 and A180667 duplicates?

[Max Alekseyev]

The description of A089068 is weird.
If q defined as in the given Mathematica code, then it is simply equal to 1.
And for matrix {{0,1,0},{0,0,1},{1,1,1}}, the characteristic
polynomial is x^3 - x^2 - x - 1, implying that the elements (3,3) of
the powers of this matrix satisfies the recurrence given in A180667.
So, these sequence are indeed duplicates.

Regards,
Max

On Wed, Sep 22, 2010 at 8:47 AM, Richard Mathar
<mathar at strw.leidenuniv.nl> wrote:
>
> Comparing
>
> http://oeis.org/classic/?q=id:A180667|id:A089068
> 0,0,1,3,6,12,23,43,80,148,273,503,926,1704,3135,5767,10608,19512,35889,66011,121414,223316,410743,755475,1389536,2555756,4700769,8646063,15902590,29249424,53798079,98950095,181997600,
> 0,1,3,6,12,23,43,80,148,273,503,926,1704,3135,5767,10608,19512,35889,66011,121414,223316,410743,755475,1389536,2555756,4700769,8646063,15902590,29249424,53798079,98950095,181997600,334745776,615693473,
>
> there is a comment in A180667 which says "For larger values of n the two sequences diverge. "
> How can this happen given that the two g.f.'s are the same?
>
> Richard Mathar
>
>
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