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%I #28 Sep 08 2022 08:45:58
%S 27,109,271,545,931,1493,2199,3145,4267,5693,7327,9329,11571,14245,
%T 17191,20633,24379,28685,33327,38593,44227,50549,57271,64745,72651,
%U 81373,90559,100625,111187,122693,134727
%N Wiener index of a benzenoid consisting of a chain of n hexagons characterized by the encoding s = 1133 (see the Gutman et al. reference, Sec. 5).
%H Vincenzo Librandi, <a href="/A193399/b193399.txt">Table of n, a(n) for n = 1..10000</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 I. Gutman, S. Klavzar, M. Petkovsek, and P. Zigert, <a href="http://match.pmf.kg.ac.rs/electronic_versions/Match43/match43_49-66.pdf">On Hosoya polynomials of benzenoid graphs</a>, Comm. Math. Comp. Chem. (MATCH), 43, 2001, 49-66.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).
%F a(n) = 4*n^3 + 16*n^2 + 8*n + 2*(-1)^n*(n - 2) - 3.
%F G.f.: x*(27 + 55*x + 26*x^2 + 2*x^3 - 21*x^4 + 7*x^5)/((1+x)^2*(1-x)^4). - _Bruno Berselli_, Jul 27 2011
%p a := proc (n) options operator, arrow: 4*n^3+16*n^2+8*n+2*(-1)^n*(n-2)-3 end proc: seq(a(n), n = 1 .. 40);
%o (Magma) [4*n^3 + 16*n^2 + 8*n + 2*(-1)^n*(n - 2) - 3: n in [1..40]]; // _Vincenzo Librandi_, Jul 26 2011
%o (PARI) a(n)=4*n^3+16*n^2+8*n+2*(-1)^n*(n-2)-3 \\ _Charles R Greathouse IV_, Jul 28 2011
%Y Cf. A143937, A143938, A193391, A193392, A193393, A193394, A193395, A193396, A193397, A193398.
%K nonn,easy
%O 1,1
%A _Emeric Deutsch_, Jul 25 2011
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