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A193392 Hyper-Wiener index of a benzenoid consisting of a spiral chain of n hexagons (s=1; see the Gutman et al. reference).

%I A193392 #32 Sep 08 2022 08:45:58
%S A193392 42,215,636,1401,2622,4427,6960,10381,14866,20607,27812,36705,47526,
%T A193392 60531,75992,94197,115450,140071,168396,200777,237582,279195,326016,
%U A193392 378461,436962,501967,573940,653361,740726,836547,941352,1055685,1180106,1315191,1461532
%N A193392 Hyper-Wiener index of a benzenoid consisting of a spiral chain of n hexagons (s=1; see the Gutman et al. reference).
%H A193392 Vincenzo Librandi, <a href="/A193392/b193392.txt">Table of n, a(n) for n = 1..10000</a>
%H A193392 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 A193392 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 A193392 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A193392 a(n) = (2*n^4 + 28*n^3 + 154*n^2 - 169*n + 111)/3.
%F A193392 G.f.: x*(42 + 5*x - 19*x^2 - 49*x^3 + 37*x^4)/(1-x)^5. - _Bruno Berselli_, Jul 27 2011
%p A193392 a := proc (n) options operator, arrow; (2/3)*n^4+(28/3)*n^3+(154/3)*n^2-(169/3)*n+37 end proc: seq(a(n), n = 1 .. 35);
%o A193392 (Magma) [(2*n^4 + 28*n^3 + 154*n^2 - 169*n + 111)/3: n in [1..40]]; // _Vincenzo Librandi_, Jul 26 2011
%o A193392 (PARI) a(n)=(2*n^4+28*n^3+154*n^2-169*n)/3+37 \\ _Charles R Greathouse IV_, Jul 26 2011
%Y A193392 Cf. A143937, A143938, A193391.
%K A193392 nonn,easy
%O A193392 1,1
%A A193392 _Emeric Deutsch_, Jul 25 2011