A304514 - OEIS

%I #24 May 16 2018 11:45:27

%S 21,87,219,483,1011,2067,4179,8403,16851,33747,67539,135123,270291,

%T 540627,1081299,2162643,4325331,8650707,17301459,34602963,69205971,

%U 138411987,276824019,553648083,1107296211,2214592467,4429184979,8858370003,17716740051,35433480147,70866960339,141733920723,283467841491,566935683027,1133871366099

%N a(n) = 33*2^n - 45 (n>=1).

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

%H Colin Barker, <a href="/A304514/b304514.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.: 3*x*(7 + 8*x) / ((1 - x)*(1 - 2*x)).

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

%F (End)

%p seq(33*2^n-45, n = 1 .. 40);

%t Rest@ CoefficientList[Series[3 x (7 + 8 x)/((1 - x) (1 - 2 x)), {x, 0, 35}], x] (* or *)

%t LinearRecurrence[{3, -2}, {21, 87}, 35] (* or *)

%t Array[33*2^# - 45 &, 35] (* _Michael De Vlieger_, May 15 2018 *)

%o (GAP) List([1..40],n->33*2^n-45); # _Muniru A Asiru_, May 15 2018

%o (PARI) a(n) = 33*2^n - 45; \\ _Altug Alkan_, May 15 2018

%o (PARI) Vec(3*x*(7 + 8*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ _Colin Barker_, May 15 2018

%Y Cf. A304513, A304515, A304516.

%K nonn,easy

%O 1,1

%A _Emeric Deutsch_, May 15 2018