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 A304388 #28 Nov 02 2021 11:22:02
%S A304388 268,556,1132,2284,4588,9196,18412,36844,73708,147436,294892,589804,
%T A304388 1179628,2359276,4718572,9437164,18874348,37748716,75497452,150994924,
%U A304388 301989868,603979756,1207959532,2415919084,4831838188,9663676396,19327352812,38654705644,77309411308
%N A304388 a(n) = 144*2^n - 20 (n>=1).
%C A304388 a(n) is the second Zagreb index of the dendrimer nanostar NS1[n], defined pictorially in the Ashrafi et al. reference (Ns1[3] is shown in Fig. 1) or in the Ahmadi et al. reference (Fig. 1).
%C A304388 The second Zagreb index of a simple connected graph is the sum of the degree products d(i)d(j) over all edges ij of the graph.
%C A304388 The M-polynomial of NS1[n] is M(NS1[n]; x,y) = xy^4 + (9*2^n +3)x^2*y^2 + (18*2^n - 12)x^2*y^3 + 3x^3*y^4.
%H A304388 Colin Barker, <a href="/A304388/b304388.txt">Table of n, a(n) for n = 1..1000</a>
%H A304388 M. B. Ahmadi and M. Sadeghimehr, <a href="https://oam-rc.inoe.ro/download.php?idu=1158=52">Atom bond connectivity index of an infinite class NS1[n] of dendrimer nanostars</a>, Optoelectronics and Advanced Materials, 4(7):1040-1042 July 2010.
%H A304388 Ali Reza Ashrafi and Parisa Nikzad, <a href="http://www.chalcogen.ro/383_Ashrafi.pdf">Kekulé index and bounds of energy for nanostar dendrimers</a>, Digest J. of Nanomaterials and Biostructures, 4, No. 2, 2009, 383-388.
%H A304388 E. Deutsch and Sandi Klavzar, <a href="http://dx.doi.org/10.22052/ijmc.2015.10106">M-polynomial and degree-based topological indices</a>, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
%H A304388 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A304388 From _Colin Barker_, May 18 2018: (Start)
%F A304388 G.f.: 4*x*(67 - 62*x) / ((1 - x)*(1 - 2*x)).
%F A304388 a(n) = 3*a(n-1) - 2*a(n-2) for n>2.
%F A304388 (End)
%p A304388 seq(144*2^n-20, n = 1 .. 40);
%t A304388 LinearRecurrence[{3,-2},{268,556},30] (* _Harvey P. Dale_, Nov 02 2021 *)
%o A304388 (PARI) a(n) = 144*2^n - 20; \\ _Altug Alkan_, May 13 2018
%o A304388 (PARI) Vec(4*x*(67 - 62*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ _Colin Barker_, May 18 2018
%o A304388 (GAP) List([1..40],n->144*2^n-20); # _Muniru A Asiru_, May 13 2018
%Y A304388 Cf. A304386, A304387, A304389.
%K A304388 nonn,easy
%O A304388 1,1
%A A304388 _Emeric Deutsch_, May 13 2018