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A193394 Hyper-Wiener index of a benzenoid consisting of a zig-zag chain of n hexagons (s=13; see the Gutman et al. reference).

%I A193394 #36 Sep 08 2022 08:45:58
%S A193394 42,215,636,1513,3118,5787,9920,15981,24498,36063,51332,71025,95926,
%T A193394 126883,164808,210677,265530,330471,406668,495353,597822,715435,
%U A193394 849616,1001853,1173698,1366767,1582740,1823361,2090438,2385843,2711512,3069445,3461706,3890423,4357788
%N A193394 Hyper-Wiener index of a benzenoid consisting of a zig-zag chain of n hexagons (s=13; see the Gutman et al. reference).
%H A193394 Vincenzo Librandi, <a href="/A193394/b193394.txt">Table of n, a(n) for n = 1..10000</a>
%H A193394 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 A193394 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 A193394 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A193394 a(n) = (8*n^4 + 24*n^3 + 28*n^2 + 147*n - 81)/3.
%F A193394 G.f.: x*(42 + 5*x - 19*x^2 + 63*x^3 - 27*x^4)/(1-x)^5. - _Bruno Berselli_, Jul 27 2011
%p A193394 a := n-> (8/3)*n^4+8*n^3+(28/3)*n^2+49*n-27: seq(a(n), n = 1 .. 35);
%t A193394 LinearRecurrence[{5,-10,10,-5,1},{42,215,636,1513,3118},40] (* _Harvey P. Dale_, Dec 10 2021 *)
%o A193394 (Magma) [(8*n^4 + 24*n^3 + 28*n^2 + 147*n - 81)/3: n in [1..40]]; // _Vincenzo Librandi_, Jul 26 2011
%o A193394 (PARI) a(n)=(8*n^2+24*n+28)*n^2/3+49*n-27 \\ _Charles R Greathouse IV_, Jul 28 2011
%Y A193394 Cf. A143937, A143938, A193391, A193392, A193393.
%K A193394 nonn,easy
%O A193394 1,1
%A A193394 _Emeric Deutsch_, Jul 25 2011