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Search: id:A141221
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| A141221 |
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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. |
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+0
3
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| 0, 30, 156, 826, 4406, 23562, 126104, 675074, 3614142, 19349430, 103593804, 554625898, 2969386478, 15897666066, 85113810056, 455687062274, 2439682811478, 13061709929934, 69930511268508, 374397872321626
(list; graph; listen)
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OFFSET
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1,2
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LINKS
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MathLinks.ro Forum, How many distinct ways that silence will occur?
G. P. Michon, Brocoum's Screaming Circles.
G. P. Michon, Silent circles, enumerated by Max Alekseyev.
G. P. Michon, A screaming game for short-sighted people.
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FORMULA
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For n>1, a(n+4) = 8 a(n+3) - 16 a(n+2) + 10 a(n+1) - a(n)
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
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EXAMPLE
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a(1)=0 because two people always make eye contact when they look at each other.
a(2)=30 because 4 people can look at each other in 30 distinct ways without making eye contact.
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CROSSREFS
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Cf. A094047, A114939.
Cf. A141384, A141385.
Sequence in context: A042760 A042762 A064240 this_sequence A159884 A074357 A140594
Adjacent sequences: A141218 A141219 A141220 this_sequence A141222 A141223 A141224
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KEYWORD
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nonn
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AUTHOR
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Max Alekseyev (maxale(AT)gmail.com), Jun 14 2008
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