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A216113 The hyper-Wiener index of the meta-polyphenyl chain with n hexagons (see the Dou et al. and the Deng references). 5

%I

%S 42,477,2241,6846,16380,33507,61467,104076,165726,251385,366597,

%T 517482,710736,953631,1254015,1620312,2061522,2587221,3207561,3933270,

%U 4775652,5746587,6858531,8124516,9558150,11173617,12985677,15009666,17261496,19757655

%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^{4n+1}-nt^5+nt-t)/(t^4-1)^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) = 3n(16n^3 + 8n^2 - 5n +9)/2.

%F G.f.: 3*x*(3*x^3-92*x^2-89*x-14)/(x-1)^5. [_Colin Barker_, Oct 30 2012]

%p seq(3*n*(16*n^3+8*n^2-5*n+9)*(1/2),n=1..30);

%t LinearRecurrence[{5, -10, 10, -5, 1}, {42, 477, 2241, 6846, 16380}, 30] (* _Jean-Fran├žois Alcover_, Sep 23 2017 *)

%Y Cf. A216108-A216112.

%K nonn,easy

%O 1,1

%A _Emeric Deutsch_, Oct 26 2012

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Last modified January 25 19:09 EST 2020. Contains 331249 sequences. (Running on oeis4.)