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%I #8 Aug 08 2014 01:39:07
%S 54,1008,6656,27340,84990,219604,497168,1019016,1932630,3443880,
%T 5830704,9458228,14795326,22432620,33101920,47697104,67296438,
%U 93186336,126886560,170176860,225125054,294116548,379885296,485546200,614628950,771113304,959465808,1184677956
%N The Szeged index of the parallelogram-shaped benzenoid Q_k (see Fig. 5.7 of the Diudea et al. reference).
%D M. V. Diudea, I. Gutman, J. Lorentz, Molecular Topology, Nova Science Publishers, Huntington, NY (2001).
%H I. Gutman, S. Klavzar, <a href="http://www.fmf.uni-lj.si/~klavzar/preprints/alg-szeged-benzi.pdf">An algorithm for the calculation of the Szeged index of benzenoid hydrocarbons</a>, preprint.
%H I. Gutman, S. Klavzar, <a href="http://dx.doi.org/10.1021/ci00028a008">An algorithm for the calculation of the Szeged index of benzenoid hydrocarbons</a>, J. Chem. Inf. Comput. Sci., 35, 1995, 1011-1014.
%H I. Gutman, P. V. Khadikar, T. Khaddar, <a href="http://match.pmf.kg.ac.rs/electronic_versions/Match35/match35_105-116.pdf">Wiener and Szeged indices of benzenoid hydrocarbons containing a linear polyacene fragment</a>, Commun. Math. Chem. (MATCH), 35, 1997, 105-116.
%F a(k) = (12k^6+72k^5+137k^92k^3+13k^2-2k)/6.
%F G.f: 2z(27+315z+367z^2+13z^3-2z^4)/(1-z)^7.
%e a(1)=54; indeed, the benzenoid consists of 1 hexagon and each of its six edges contributes 3*3 towards the Szeged index; 6*9 = 54.
%p a := proc (n) options operator, arrow: 2*n^6+12*n^5+(137/6)*n^4+(46/3)*n^3+(13/6)*n^2-(1/3)*n end proc: seq(a(n), n = 1 .. 30);
%K nonn
%O 1,1
%A _Emeric Deutsch_, Aug 07 2014
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