A228606 - OEIS

%I #12 Sep 01 2019 18:26:27

%S 1,18,299,4957,82176,1362293,22583749,374387682,6206504351,

%T 102889860193,1705682092824,28276366556657,468758456813401,

%U 7770959199931218,128824997201136899,2135628238019808757,35403905065928790576,586916988454650778493,9729761468267561700349,161297526041365993456482

%N The Merrifield-Simmons index of the para-polyphenylene chain of length n.

%C The Merrifield-Simmons index of a graph is the number of its independent vertex subsets.

%D R. E. Merrifield, H. E. Simmons, Topological Methods in Chemistry, Wiley, New York, 1989.

%H 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 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (17,-7).

%F 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 G.f.: (1+x)/(1-17*x+7*x^2).

%p gser := series((x+1)/(7*x^2-17*x+1), x = 0, 22): seq(coeff(gser, x, n), n = 0 .. 20);

%Y Cf. A228604, A228605

%K nonn

%O 0,2

%A _Emeric Deutsch_, Nov 23 2013