2n people in a circle without an eye contact

[Max Alekseyev]

I've just submitted the following sequence based on a problem at
MathLinks.ro forum.
Could anybody please double-check the listed values (not using the
given formula) and/or my solution at MathLinks.ro ?

Thanks,
Max

%I A141221
%S A141221 0, 30, 156, 826, 4406, 23562, 126104, 675074, 3614142,
19349430, 103593804, 554625898, 2969386478, 15897666066, 85113810056,
455687062274, 2439682811478, 13061709929934, 69930511268508,
374397872321626, 2004472214764742, 10731655163727066,
57455734085528408, 307609714339920002, 1646898048773411406,
8817254646440128230, 47206309800460114956, 252735774834033062026,
1353110890280530527806, 7244360568257876251362
%N A141221 Number of ways for each of 2n (labeled) people in a circle
to look at either a neighbor or the diametrally opposite person, such
that no eye contact occurs.
%H A141221 <a href="http://www.mathlinks.ro/viewtopic.php?t=209344">How
many distinct ways that silence will occur?</a>, a problem at
MathLinks.ro forum.
%F A141221 For n>1, a(n+4) = 8 a(n+3) - 16 a(n+2) + 10 a(n+1) - a(n)
%Y A141221 Cf. A094047, A114939.
%O A141221 1
%K A141221 ,nonn,
%A A141221 Max Alekseyev (maxal at cs.ucsd.edu), Jun 14 2008




Given that A127275 and A120011 are almost the same, and that the
generating functions are described in some detail, it seems to be manageable
to simplify A120011 based on this, and to show that they only differ
by the additional leading number in A127275.

Richard