Simple Conjecture

[creigh at o2online.de]

I would like to know if the conjecture made in the
comment, below, has already been proven or at least has
a name. 

Sincerely,
Creighton 

%I A098149 
%S A098149 -1 -1 4 -11 29 -76 199 -521 1364 -3571 9349 -24476 64079 -167761 
439204 -1149851 
%N A098149 Sequence relates bisections of Lucas and Fibonacci numbers. 
%C A098149 2*a(n) + A098150(n) = 
8*(-1)^(n+1)*A001519(n) - (-1)^(n+1)*A005248(n+1) 
Apparently (not sure if this is a conjecture or has been proven 
by someone else) if (z(n)) is any sequence of integers (not all zero) 
satisfying the forumla z(n) = 2(z(n-2) - z(n-1)) + z(n-3) then 
|z(n+1)/z(n)| -> golden ratio phi + 1 = (3+sqrt(5))/2 
%H A098149 C. Dement, <a href="http://www.crowdog.de">The Floretions<
/a>. 
%F A098149 a(n) = 2(a(n-2) - a(n-1)) + a(n-3) 
%o A098149 Floretion Algebra Multiplication Program 
%Y A098149 Cf. A098150, A001519, A005248 
%O A098149 0 
%K A098149 ,easy,sign, 
%A A098149 Creighton Dement (creigh at o2online.de), Aug 29 2004