%I A141221
%S A141221 0,30,156,826,4406,23562,126104,675074,3614142,19349430,103593804,
%T A141221 554625898,2969386478,15897666066,85113810056,455687062274,
%U A141221 2439682811478,13061709929934,69930511268508,374397872321626
%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 MathLinks.ro Forum, <a href="http://www.mathlinks.ro/viewtopic.php?t=209344">
               How many distinct ways that silence will occur?</a>
%H A141221 G. P. Michon, <a href="http://www.numericana.com/answer/counting.htm#scream">
               Brocoum's Screaming Circles</a>.
%H A141221 G. P. Michon, <a href="http://www.numericana.com/answer/graphs.htm#alekseyev">
               Silent circles</a>, enumerated by Max Alekseyev.
%H A141221 G. P. Michon, <a href="http://www.numericana.com/answer/graphs.htm#prisms">
               A screaming game for short-sighted people</a>.
%F A141221 For n>1, a(n+4) = 8 a(n+3) - 16 a(n+2) + 10 a(n+1) - a(n)
%F A141221 O.g.f.: 2x^2(-15+42x-29x^2+3x^3)/((1-x)(x^3-9x^2+7x-1)). - R. J. Mathar 
               (mathar(AT)strw.leidenuniv.nl), Jun 16 2008
%e A141221 a(1)=0 because two people always make eye contact when they look at each 
               other.
%e A141221 a(2)=30 because 4 people can look at each other in 30 distinct ways without 
               making eye contact.
%Y A141221 Cf. A094047, A114939.
%Y A141221 Cf. A141384, A141385.
%Y A141221 Sequence in context: A042760 A042762 A064240 this_sequence A159884 A074357 
               A140594
%Y A141221 Adjacent sequences: A141218 A141219 A141220 this_sequence A141222 A141223 
               A141224
%K A141221 nonn
%O A141221 1,2
%A A141221 Max Alekseyev (maxale(AT)gmail.com), Jun 14 2008