Problem

[g_m at mcraefamily.com]

This sequence is A002878, which already contains the formula,
a(n+1)=3*a(n)-a(n-1).


Original Message:
-----------------
From: Max Alekseyev maxale at gmail.com
Date: Fri, 16 Nov 2007 12:20:36 -0800
To: grafix at csl.pl, seqfan at ext.jussieu.fr, petsie at dordos.net
Subject: Re: Problem

Oh, it turns out that this can be reduced to the second order
recurrence (as noticed by Zak Seidov).
The characteristic polynomial here has the following factorization:

t^6 - 18 t^3 + 1 = (t^2 - 3t + 1) * (t^4 + 3 t^3 + 8 t^2 + 3 t + 1)

and the initial conditions are well consistent with the first factor
t^2 - 3t + 1. Therefore, our sequence also satisfies a simpler
recurrence:
n(j) = 3*n(j-1) - n(j-2)
with
n(0)=1, n(1)=4.

Max


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