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%I #11 Jun 17 2017 03:06:27
%S 42,477,1953,5442,12240,23967,42567,70308,109782,163905,235917,329382,
%T 448188,596547,778995,1000392,1265922,1581093,1951737,2384010,2884392,
%U 3459687,4117023,4863852,5707950,6657417,7720677,8906478,10223892,11682315
%N The hyper-Wiener index of the meta-polyphenyl chain with n hexagons (see the Dou et al. and the Deng references).
%C The Hosoya-Wiener polynomial of the graph is n(6+6t+6t^2+3t^3)+(1+2t+2t^2+t^3)^2*(t^{3n+1}-nt^4+nt-t)/(t^3-1)^2.
%D Y. Dou, H. Bian, H. Gao, and H. Yu, The polyphenyl chains with extremal edge-Wiener indices, MATCH Commun. Math. Comput. Chem., 64, 2010, 757-766.
%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_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = 3*n*(-13+14*n+18*n^2+9*n^3)/2.
%F G.f.: -3*x*(9*x^3-4*x^2+89*x+14)/(x-1)^5. [_Colin Barker_, Oct 30 2012]
%p seq(3*n*(9*n^3+18*n^2+14*n-13)*(1/2), n=1..30);
%Y Cf. A216108, A216109, A216110, A216112, A216113.
%K nonn,easy
%O 1,1
%A _Emeric Deutsch_, Oct 26 2012
%E Typo corrected in first formula by _Colin Barker_, Oct 30 2012