Scaled Chebyshev U-polynomials evaluated at sqrt(3)/2

[Creighton Dement]

Dear Seqfans, 

I noticed that the two sequences, below, have some rather obvious
properties in common as described in the Comments entry (also given,
below. Note that  "strictly increasing" needs to be replaced by
"increasing", etc.) of A105660. If the link to
http://www.crowdog.de/SeqContext/FiveSigns.html given for A105660 is
followed one is perhaps inclined to suspect that this is some general
property of a certain class of sequences. I found it aesthetic that
several of the sequences from the link (which are all interlinked
through various identities) also have similar properties.  

Can someone find more in common between these two sequences (or confirm
that they belong to a more general class of sequences with those
properties)? 

Thanks and sincerely, 
Creighton 

http://www.research.att.com/projects/OEIS?Anum=A057083
Scaled Chebyshev U-polynomials evaluated at sqrt(3)/2; expansion of
1/(1-3*x+3*x^2).

1,3,6,9,9,0,-27,-81,-162,-243,-243,0,729,2187,4374,6561,           
6561,0,-19683,-59049,-118098,-177147,-177147,0,531441,           
1594323,3188646,4782969,4782969,0,-14348907,-43046721,           
-86093442,-129140163,-129140163,0

(=  ((-1)^n)*A105660 ; Smith College Diploma Problem)

and 

http://www.research.att.com/projects/OEIS?Anum=A105660 

3,10,27,49,0,-485,-2643,-9602,-26163,-47525,0,470449,           
2563707,9313930,25378083,46099201,0,-456335045,-2486793147,           
-9034502498,-24616714347,-44716177445,0 
Name:      G.f. (1-x)(x^2-5x+3)/(x^4-6x^3+13x^2-6x+1).

Comments:  One of a set of interlinked sequences which appear to have
the property that if a(m) = 0 for some m, then a(m+1), a(m+2), a(m+3),
a(m+4), a(m+5) are strictly increasing or decreasing and a(m+6) = 0.
Furthermore, for               this particular sequence it would appear
that a(m+3) is always even with a(m+1), a(m+2), a(m+4), a(m+5) odd.
(a(n)) sequence is "ves" in  the link to sequences in context. The
identity ves = jes + les + tes holds.