%I #15 Feb 12 2021 12:00:11

%S 25,145,385,865,1825,3745,7585,15265,30625,61345,122785,245665,491425,

%T 982945,1965985,3932065,7864225,15728545,31457185,62914465,125829025,

%U 251658145,503316385,1006632865,2013265825,4026531745,8053063585,16106127265,32212254625,64424509345,128849018785

%N a(n) = 120*2^n - 95.

%C 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 Colin Barker, <a href="/A305269/b305269.txt">Table of n, a(n) for n = 0..1000</a>

%H 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 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).

%F From _Colin Barker_, May 31 2018: (Start)

%F G.f.: 5*(5 + 14*x) / ((1 - x)*(1 - 2*x)).

%F a(n) = 3*a(n-1) - 2*a(n-2) for n>1.

%F (End)

%p seq(120*2^n-95, n = 0..40);

%o (PARI) Vec(5*(5 + 14*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ _Colin Barker_, May 31 2018

%Y Cf. A305270, A305271, A305272.

%K nonn,easy

%O 0,1

%A _Emeric Deutsch_, May 30 2018