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%I #17 Dec 09 2016 03:42:34
%S 27,109,279,569,1011,1637,2479,3569,4939,6621,8647,11049,13859,17109,
%T 20831,25057,29819,35149,41079,47641,54867,62789,71439,80849,91051,
%U 102077,113959,126729,140419,155061,170687,187329,205019,223789,243671
%N The Wiener index of a benzenoid consisting of a linear chain of n hexagons.
%H G. C. Greubel, <a href="/A143938/b143938.txt">Table of n, a(n) for n = 1..1000</a>
%H A. A. Dobrynin, I. Gutman, S. Klavzar, P. Zigert, <a href="http://www.fmf.uni-lj.si/~klavzar/preprints/Wiener-survey.pdf">Wiener Index of Hexagonal Systems</a>, Acta Applicandae Mathematicae 72 (2002), pp. 247-294.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = (1/3)*(16*n^3 + 36*n^2 + 26*n + 3).
%F G.f.: z*(27+z+5*z^2-z^3)/(1-z)^4.
%F a(n) = Sum_{k=1,..,2*n+1} k*A143937(n,k).
%e a(1)=27 because in a hexagon we have 6 distances equal to 1, 6 distances equal to 2 and 3 distances equal to 3 (6*1+6*2+3*3=27).
%p seq((16*n^3+36*n^2+26*n+3)*1/3, n = 1 .. 35)
%t Table[(1/3)*(16*n^3 + 36*n^2 + 26*n + 3), {n, 1,50}] (* or *) LinearRecurrence[{4,-6,4,-1}, {27,109,279,569}, 50] (* _G. C. Greubel_, Dec 08 2016 *)
%Y Cf. A143937.
%K nonn,easy
%O 1,1
%A _Emeric Deutsch_, Sep 06 2008
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