%I
%S 27,198,621,1404,2655,4482,6993,10296,14499,19710,26037,33588,42471,
%T 52794,64665,78192,93483,110646,129789,151020,174447,200178,228321,
%U 258984,292275,328302,367173,408996,453879,501930
%N The Wiener index of the metapolyphenyl chain with n hexagons (see the Dou et al. and the Deng references).
%C The HosoyaWiener polynomial of the graph is n(6+6t+6t^2+3t^3)+(1+2t+2t^2+t^3)^2*(t^{3n+1}nt^4+ntt)/(t^31)^2.
%D Y. Dou, H. Bian, H. Gao, and H. Yu, The polyphenyl chains with extremal edgeWiener indices, MATCH Commun. Math. Comput. Chem., 64, 2010, 757766.
%H H. Deng, <a href="http://arxiv.org/abs/1006.5488">Wiener indices of spiro and polyphenyl hexagonal chains</a>, arXiv:1006.5488
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,6,4,1).
%F a(n) = 18n^3 + 18n^2 9n.
%F G.f.: 9*x*(x^210*x3)/(x1)^4. [_Colin Barker_, Oct 30 2012]
%e a(1)=27 because the graph consists of 1 hexagon and the Wiener index is 6*1+6*2+3*3=27.
%p seq(18*n^3+18*n^29*n,n=1..30);
%Y Cf. A216108, A216109, A216111A216113.
%K nonn,easy
%O 1,1
%A _Emeric Deutsch_, Oct 26 2012
