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A193397 Wiener index of a benzenoid consisting of a double-step spiral chain of n hexagons (n>=2, s=21; see the Gutman et al. reference).

%I A193397 #31 Sep 08 2022 08:45:58
%S A193397 109,271,553,955,1541,2279,3265,4435,5917,7615,9689,12011,14773,17815,
%T A193397 21361,25219,29645,34415,39817,45595,52069,58951,66593,74675,83581,
%U A193397 92959,103225,113995,125717,137975,151249,165091,180013,195535,212201,229499,248005,267175,287617
%N A193397 Wiener index of a benzenoid consisting of a double-step spiral chain of n hexagons (n>=2, s=21; see the Gutman et al. reference).
%H A193397 Vincenzo Librandi, <a href="/A193397/b193397.txt">Table of n, a(n) for n = 2..10000</a>
%H A193397 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 A193397 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 A193397 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).
%F A193397 a(n) = 4*n^3 + 20*n^2 - 12*n + 2*(-1)^n*(n-2) + 21.
%F A193397 G.f.: x^2*(109+53*x-98*x^2+14*x^3+53*x^4-35*x^5)/((1+x)^2*(1-x)^4). - _Bruno Berselli_, Jul 27 2011
%F A193397 a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6), with a(2)=109, a(3)=271, a(4)=553, a(5)=955, a(6)=1541, a(7)=2279. - _Harvey P. Dale_, Aug 26 2011
%p A193397 a := proc (n) options operator, arrow: 4*n^3+20*n^2-12*n+2*(-1)^n*(n-2)+21 end proc: seq(a(n), n = 2 .. 40);
%t A193397 Table[4n^3+20n^2-12n+2(-1)^n(n-2)+21,{n,2,40}] (* or *) LinearRecurrence[ {2,1,-4,1,2,-1},{109,271,553,955,1541,2279},39] (* _Harvey P. Dale_, Aug 26 2011 *)
%o A193397 (Magma) [4*n^3 + 20*n^2 - 12*n + 2*(-1)^n*(n-2) + 21: n in [2..40]]; // _Vincenzo Librandi_, Jul 26 2011
%Y A193397 Cf. A143937, A143938, A193391, A193392, A193393, A193394, A193395, A193396.
%K A193397 nonn,easy
%O A193397 2,1
%A A193397 _Emeric Deutsch_, Jul 25 2011