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 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. 3
 0, 30, 156, 826, 4406, 23562, 126104, 675074, 3614142, 19349430, 103593804, 554625898, 2969386478, 15897666066, 85113810056, 455687062274, 2439682811478, 13061709929934, 69930511268508, 374397872321626 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Max A. Alekseyev and 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 short-sighted people. Index entries for linear recurrences with constant coefficients, signature (8,-16,10,-1). FORMULA a(n) = 8*a(n-1) - 16*a(n-2) + 10*a(n-3) - a(n-4), for n > 1. O.g.f.: 2*x^2*(15 -42*x +29*x^2 -3*x^3)/((1-x)*(1-7*x+9*x^2-x^3)). - R. J. Mathar, Jun 16 2008 a(n) = -7*[n=1] + (A141385(n) - 1). - G. C. Greubel, Mar 31 2021 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]] (* Jean-François Alcover, Dec 14 2018 *) PROG (Magma) I:=[30, 156, 826, 4406]; [0] cat [n le 4 select I[n] else 8*Self(n-1) -16*Self(n-2) +10*Self(n-3) -Self(n-4): n in [1..30]]; // G. C. Greubel, Mar 31 2021 (Sage) def A141221_list(prec):     P. = PowerSeriesRing(QQ, prec)     return P( 2*x^2*(15 -42*x +29*x^2 -3*x^3)/((1-x)*(1-7*x+9*x^2-x^3)) ).list() a=A141221_list(30); a[1; ] # G. C. Greubel, Mar 31 2021 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

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Last modified July 25 02:57 EDT 2021. Contains 346282 sequences. (Running on oeis4.)