This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A245830 #15 Dec 09 2016 03:50:01
%S A245830 54,243,656,1381,2506,4119,6308,9161,12766,17211,22584,28973,36466,
%T A245830 45151,55116,66449,79238,93571,109536,127221,146714,168103,191476,
%U A245830 216921,244526,274379,306568,341181,378306,418031
%N A245830 The Szeged index of a benzenoid consisting of a linear chain of n hexagons.
%D A245830 M. V. Diudea, I. Gutman, J. Lorentz, Molecular Topology, Nova Science Publishers, Huntington, NY (2001).
%H A245830 G. C. Greubel, <a href="/A245830/b245830.txt">Table of n, a(n) for n = 1..1000</a>
%H A245830 I. Gutman, S. Klavzar, <a href="http://www.fmf.uni-lj.si/~klavzar/preprints/alg-szeged-benzi.pdf">An algorithm for the calculation of the Szeged index of benzenoid hydrocarbons</a>, preprint.
%H A245830 I. Gutman, S. Klavzar, <a href="http://dx.doi.org/10.1021/ci00028a008">An algorithm for the calculation of the Szeged index of benzenoid hydrocarbons</a>, J. Chem. Inf. Comput. Sci., 35, 1995, 1011-1014.
%H A245830 I. Gutman, P. V. Khadikar, T. Khaddar, <a href="http://match.pmf.kg.ac.rs/electronic_versions/Match35/match35_105-116.pdf">Wiener and Szeged indices of benzenoid hydrocarbons containing a linear polyacene fragment</a>, Commun. Math. Chem. (MATCH), 35, 1997, 105-116.
%H A245830 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A245830 a(n) = (44*n^3 + 72*n^2 + 43*n + 3)/3.
%F A245830 G.f.: z*(54 + 27*z + 8*z^2 - z^3)/(1-z)^4.
%F A245830 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - _G. C. Greubel_, Dec 08 2016
%e A245830 a(1)=54; indeed, the benzenoid consists of 1 hexagon and each of its six edges contributes 3*3 towards the Szeged index; 6*9 = 54.
%p A245830 a := proc (n) options operator, arrow: (44/3)*n^3+24*n^2+(43/3)*n+1 end proc: seq(a(n), n = 1 .. 30);
%t A245830 LinearRecurrence[{4, -6, 4, -1}, {54, 243, 656, 1381}, 100] (* or *) Table[(44*n^3 + 72*n^2 + 43*n + 3)/3, {n,1,100}] (* _G, C, Greubel_, Dec 08 2016 *)
%o A245830 (PARI) Vec(z*(54 + 27*z + 8*z^2 - z^3)/(1-z)^4 + O(x^50)) \\ _G. C. Greubel_, Dec 08 2016
%Y A245830 Cf. A143938.
%K A245830 nonn,easy
%O A245830 1,1
%A A245830 _Emeric Deutsch_, Aug 07 2014