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A193395 Wiener index of a benzenoid consisting of a double-step zig-zag chain of n hexagons (n >= 2, s = 2123; see the Gutman et al. reference).

%I A193395 #34 Mar 27 2024 08:59:19
%S A193395 109,271,553,971,1573,2375,3425,4739,6365,8319,10649,13371,16533,
%T A193395 20151,24273,28915,34125,39919,46345,53419,61189,69671,78913,88931,
%U A193395 99773,111455,124025,137499,151925,167319,183729,201171,219693,239311,260073,281995,305125,329479,355105
%N A193395 Wiener index of a benzenoid consisting of a double-step zig-zag chain of n hexagons (n >= 2, s = 2123; see the Gutman et al. reference).
%H A193395 Vincenzo Librandi, <a href="/A193395/b193395.txt">Table of n, a(n) for n = 2..10000</a>
%H A193395 A. A. Dobrynin, I. Gutman, S. Klavzar, and 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 A193395 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 A193395 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-2,3,-1).
%F A193395 a(n) = (16*n^3 + 24*n^2 + 74*n +6*(-1)^n - 51)/3.
%F A193395 G.f.: x^2*(109 - 56*x - 42*x^2 + 72*x^3 - 19*x^4)/((1+x)*(1-x)^4). - _Bruno Berselli_, Jul 27 2011
%p A193395 a := proc (n) options operator, arrow; (16/3)*n^3+8*n^2+(74/3)*n+2*(-1)^n-17 end proc: seq(a(n), n = 2 .. 40);
%t A193395 Table[(16n^3+24n^2+74n+6(-1)^n-51)/3,{n,2,40}] (* or *) LinearRecurrence[ {3,-2,-2,3,-1},{109,271,553,971,1573},40] (* _Harvey P. Dale_, Apr 08 2020 *)
%o A193395 (Magma) [(16*n^3 + 24*n^2 + 74*n +6*(-1)^n - 51)/3: n in [2..40]]; // _Vincenzo Librandi_, Jul 26 2011
%o A193395 (PARI) a(n)=(16*n^3+24*n^2+74*n+6*(-1)^n)/3-17 \\ _Charles R Greathouse IV_, Jul 28 2011
%Y A193395 Cf. A143937, A143938, A193391, A193392, A193393, A193394.
%K A193395 nonn,easy
%O A193395 2,1
%A A193395 _Emeric Deutsch_, Jul 25 2011