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A193393 Wiener index of a benzenoid consisting of a zig-zag chain of n hexagons (s=13; see the Gutman et al. reference).

%I A193393 #33 Sep 08 2022 08:45:58
%S A193393 27,109,271,545,963,1557,2359,3401,4715,6333,8287,10609,13331,16485,
%T A193393 20103,24217,28859,34061,39855,46273,53347,61109,69591,78825,88843,
%U A193393 99677,111359,123921,137395,151813,167207,183609,201051,219565,239183,259937,281859,304981,329335,354953
%N A193393 Wiener index of a benzenoid consisting of a zig-zag chain of n hexagons (s=13; see the Gutman et al. reference).
%H A193393 Vincenzo Librandi, <a href="/A193393/b193393.txt">Table of n, a(n) for n = 1..10000</a>
%H A193393 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 A193393 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 A193393 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A193393 a(n) = (16*n^3 + 24*n^2 + 62*n - 21)/3.
%F A193393 G.f.: x*(27 + x - 3*x^2 + 7*x^3)/(1-x)^4. - _Bruno Berselli_, Jul 27 2011
%o A193393 (Magma) [(16*n^3 + 24*n^2 + 62*n - 21)/3: n in [1..40]]; // _Vincenzo Librandi_, Jul 26 2011
%o A193393 (PARI) a(n)=(16*n^3+24*n^2+62*n)/3-7 \\ _Charles R Greathouse IV_, Jul 26 2011
%Y A193393 Cf. A143937, A143938, A193391.
%K A193393 nonn,easy
%O A193393 1,1
%A A193393 _Emeric Deutsch_, Jul 25 2011