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A304517 a(n) = 16*2^n - 11 (n>=1).

%I A304517 #23 May 16 2018 11:32:41
%S A304517 21,53,117,245,501,1013,2037,4085,8181,16373,32757,65525,131061,
%T A304517 262133,524277,1048565,2097141,4194293,8388597,16777205,33554421,
%U A304517 67108853,134217717,268435445,536870901,1073741813,2147483637,4294967285,8589934581,17179869173,34359738357,68719476725,137438953461,274877906933,549755813877
%N A304517 a(n) = 16*2^n - 11 (n>=1).
%C A304517 a(n) is the number of edges of the nanostar dendrimer NS2[n] from the Madanshekaf et al. reference.
%H A304517 Colin Barker, <a href="/A304517/b304517.txt">Table of n, a(n) for n = 1..1000</a>
%H A304517 A. Madanshekaf and M. Moradi, <a href="http://dx.doi.org/10.22052/ijmc.2014.5541">The first geometric-arithmetic index of some nanostar dendrimers</a>, Iranian J. Math. Chemistry, 5, Supplement 1, 2014, s1-s6.
%H A304517 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A304517 From _Colin Barker_, May 15 2018: (Start)
%F A304517 G.f.: x*(21 - 10*x) / ((1 - x)*(1 - 2*x)).
%F A304517 a(n) = 3*a(n-1) - 2*a(n-2) for n>2.
%F A304517 (End)
%p A304517 seq(16*2^n-11, n = 1 .. 40);
%t A304517 Rest@ CoefficientList[Series[x (21 - 10 x)/((1 - x) (1 - 2 x)), {x, 0, 35}], x] (* or *)
%t A304517 LinearRecurrence[{3, -2}, {21, 53}, 35] (* or *)
%t A304517 Array[16*2^# - 11 &, 35] (* _Michael De Vlieger_, May 15 2018 *)
%o A304517 (GAP) List([1..40],n->16*2^n-11); # _Muniru A Asiru_, May 15 2018
%o A304517 (PARI) Vec(x*(21 - 10*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ _Colin Barker_, May 15 2018
%Y A304517 Cf. A304518, A304518.
%Y A304517 First bisection of A164096 without 5. First column of the table in A224701.
%K A304517 nonn,easy
%O A304517 1,1
%A A304517 _Emeric Deutsch_, May 15 2018