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 A305269 #15 Feb 12 2021 12:00:11 %S A305269 25,145,385,865,1825,3745,7585,15265,30625,61345,122785,245665,491425, %T A305269 982945,1965985,3932065,7864225,15728545,31457185,62914465,125829025, %U A305269 251658145,503316385,1006632865,2013265825,4026531745,8053063585,16106127265,32212254625,64424509345,128849018785 %N A305269 a(n) = 120*2^n - 95. %C A305269 a(n) is the number of vertices in the polyphenylene dendrimer G[n], defined pictorially in the Arif et al. reference (see Fig. 1, where G[2] is shown). %H A305269 Colin Barker, <a href="/A305269/b305269.txt">Table of n, a(n) for n = 0..1000</a> %H A305269 N. E. Arif, Roslan Hasni and Saeid Alikhani, <a href="http://dx.doi.org/10.3923/jas.2012.2279.2282">Fourth order and fourth sum connectivity indices of polyphenylene dendrimers</a>, J. Applied Science, 12 (21), 2012, 2279-2282. %H A305269 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2). %F A305269 From _Colin Barker_, May 31 2018: (Start) %F A305269 G.f.: 5*(5 + 14*x) / ((1 - x)*(1 - 2*x)). %F A305269 a(n) = 3*a(n-1) - 2*a(n-2) for n>1. %F A305269 (End) %p A305269 seq(120*2^n-95, n = 0..40); %o A305269 (PARI) Vec(5*(5 + 14*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ _Colin Barker_, May 31 2018 %Y A305269 Cf. A305270, A305271, A305272. %K A305269 nonn,easy %O A305269 0,1 %A A305269 _Emeric Deutsch_, May 30 2018