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%I A228606 #12 Sep 01 2019 18:26:27
%S A228606 1,18,299,4957,82176,1362293,22583749,374387682,6206504351,
%T A228606 102889860193,1705682092824,28276366556657,468758456813401,
%U A228606 7770959199931218,128824997201136899,2135628238019808757,35403905065928790576,586916988454650778493,9729761468267561700349,161297526041365993456482
%N A228606 The Merrifield-Simmons index of the para-polyphenylene chain of length n.
%C A228606 The Merrifield-Simmons index of a graph is the number of its independent vertex subsets.
%D A228606 R. E. Merrifield, H. E. Simmons, Topological Methods in Chemistry, Wiley, New York, 1989.
%H A228606 T. Doslic, M. S. Litz, <a href="http://match.pmf.kg.ac.rs/electronic_versions/Match67/n2/match67n2_313-330.pdf">Matchings and independent sets in polyphenylene chains</a>, MATCH, Commun. Math. Comput. Chem., 67, 2012, 313-330.
%H A228606 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (17,-7).
%F A228606 a(n) = ((19+3*sqrt(29))*(17+3*sqrt(29))^n - (19-3*sqrt(29))*(17-3*sqrt(29))^n)/(6*2^n*sqrt(29)).
%F A228606 G.f.: (1+x)/(1-17*x+7*x^2).
%p A228606 gser := series((x+1)/(7*x^2-17*x+1), x = 0, 22): seq(coeff(gser, x, n), n = 0 .. 20);
%Y A228606 Cf. A228604, A228605
%K A228606 nonn
%O A228606 0,2
%A A228606 _Emeric Deutsch_, Nov 23 2013

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