

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.


2



0, 30, 156, 826, 4406, 23562, 126104, 675074, 3614142, 19349430, 103593804, 554625898, 2969386478, 15897666066, 85113810056, 455687062274, 2439682811478, 13061709929934, 69930511268508, 374397872321626
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..20.
Max A. Alekseyev, Gérard P. Michon, Making Walks Count: From Silent Circles to Hamiltonian Cycles, arXiv:1602.01396 [math.CO], 2016.
Art of Problem Solving 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 shortsighted people.


FORMULA

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+42x29x^2+3x^3)/((1x)(x^39x^2+7x1)).  R. J. Mathar, Jun 16 2008


EXAMPLE

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.


MATHEMATICA

Join[{0}, LinearRecurrence[{8, 16, 10, 1}, {30, 156, 826, 4406}, 20]] (* JeanFrançois Alcover, Dec 14 2018 *)


CROSSREFS

Cf. A094047, A114939.
Cf. A141384, A141385.
Sequence in context: A042760 A042762 A064240 * A159884 A074357 A140594
Adjacent sequences: A141218 A141219 A141220 * A141222 A141223 A141224


KEYWORD

nonn


AUTHOR

Max Alekseyev, Jun 14 2008


STATUS

approved



