%I #23 May 16 2018 11:45:23

%S 19,76,190,418,874,1786,3610,7258,14554,29146,58330,116698,233434,

%T 466906,933850,1867738,3735514,7471066,14942170,29884378,59768794,

%U 119537626,239075290,478150618,956301274,1912602586,3825205210,7650410458,15300820954,30601641946,61203283930,122406567898,244813135834,489626271706

%N a(n) = 57*2^(n-1) - 38 (n >= 1).

%C a(n) is the number of vertices of the nanostar dendrimer D[n] from the Ghorbani et al. reference.

%H Colin Barker, <a href="/A304513/b304513.txt">Table of n, a(n) for n = 1..1000</a>

%H M. Ghorbani and M. Songhori, <a href="http://dx.doi.org/10.22052/ijmc.2010.5155">Some topological indices of nanostar dendrimers</a>, Iranian J. Math. Chemistry, 1, No. 2, 2010, 57-65.

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

%F From _Colin Barker_, May 15 2018: (Start)

%F G.f.: 19*x*(1 + x) / ((1 - x)*(1 - 2*x)).

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

%F (End)

%p seq(57*2^(n-1)-38, n = 1 .. 40);

%t Rest@ CoefficientList[Series[19 x (1 + x)/((1 - x) (1 - 2 x)), {x, 0, 31}], x] (* or *)

%t LinearRecurrence[{3, -2}, {19, 76}, 31] (* or *)

%t Array[57*2^(# - 1) - 38 &, 31] (* _Michael De Vlieger_, May 15 2018 *)

%o (GAP) List([1..40],n->57*2^(n-1)-38); # _Muniru A Asiru_, May 15 2018

%o (PARI) Vec(19*x*(1 + x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ _Colin Barker_, May 15 2018

%Y Cf. A304514, A304515, A304516.

%K nonn,easy

%O 1,1

%A _Emeric Deutsch_, May 15 2018