A228604 - OEIS

%I #17 Sep 01 2019 18:28:11

%S 1,18,299,4932,81301,1340118,22089599,364109832,6001737001,

%T 98928520218,1630669938899,26878845894732,443052477632701,

%U 7302973450020318,120377210159548199,1984215446621359632,32706447785195768401,539110673967989840418,8886330936793922917499

%N The Merrifield-Simmons index of the ortho-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 (18,-25).

%F a(n) = ((9 + 2*sqrt(14))^(n+1) - (9 - 2*sqrt(14))^(n+1))/(4*sqrt(14)).

%F G.f. = 1/(1 - 18*x + 25*x^2).

%F a(n) = 18*a(n-1) - 25*a(n-2); a(0)=1, a(1)=18. - _Harvey P. Dale_, Nov 06 2014

%p gser := series(1/(25*x^2-18*x+1), x = 0, 22): seq(coeff(gser, x, n), n = 0 .. 20);

%t CoefficientList[Series[1/(1-18x+25x^2),{x,0,20}],x] (* or *) LinearRecurrence[ {18,-25},{1,18},20] (* _Harvey P. Dale_, Nov 06 2014 *)

%Y Cf. A228605, A228606.

%K nonn

%O 0,2

%A _Emeric Deutsch_, Nov 23 2013