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A216110 The Wiener index of the meta-polyphenyl chain with n hexagons (see the Dou et al. and the Deng references). 3

%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 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_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^2-10*x-3)/(x-1)^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^2-9*n,n=1..30);

%Y Cf. A216108, A216109, A216111-A216113.

%K nonn,easy

%O 1,1

%A _Emeric Deutsch_, Oct 26 2012

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Last modified December 12 12:30 EST 2019. Contains 329958 sequences. (Running on oeis4.)