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%I #20 Sep 23 2017 11:30:46
%S 42,477,1701,4254,8820,16227,27447,43596,65934,95865,134937,184842,
%T 247416,324639,418635,531672,666162,824661,1009869,1224630,1471932,
%U 1754907,2076831,2441124,2851350,3311217,3824577,4395426,5027904,5726295
%N The hyper-Wiener index of the ortho-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^{2n+1}-nt^3+nt-t)/(t^2-1)^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*(28+123*n+127*n^2+36*n^3+4*n^4)/2 = 3*(n+1)(4*n^3+32*n^2+95*n+28)/2.
%F G.f.: -3*(33*x^3-88*x^2+89*x+14)/(x-1)^5. [_Colin Barker_, Oct 29 2012]
%p seq(3*n*(4*n^3+20*n^2+43*n-39)*(1/2), n=1..30);
%t LinearRecurrence[{5, -10, 10, -5, 1}, {42, 477, 1701, 4254, 8820}, 30] (* _Jean-François Alcover_, Sep 23 2017 *)
%Y Cf. A216108, A216110-A216113.
%K nonn,easy
%O 0,1
%A _Emeric Deutsch_, Oct 26 2012
%E First formula corrected by _Colin Barker_, Oct 29 2012
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