cp's OEIS Frontend

A304387 a(n) = 27*2^n - 5.

%I A304387 #30 Jan 12 2019 20:03:57
%S A304387 22,49,103,211,427,859,1723,3451,6907,13819,27643,55291,110587,221179,
%T A304387 442363,884731,1769467,3538939,7077883,14155771,28311547,56623099,
%U A304387 113246203,226492411,452984827,905969659,1811939323,3623878651,7247757307,14495514619,28991029243,57982058491
%N A304387 a(n) = 27*2^n - 5.
%C A304387 For n>0, a(n) is the number of edges in the dendrimer nanostar NS1[n] defined pictorially in the Ashrafi et al. reference (Ns1[3] is shown in Fig. 1) or in the Ahmadi et al. reference (Fig. 1).
%H A304387 Colin Barker, <a href="/A304387/b304387.txt">Table of n, a(n) for n = 0..1000</a>
%H A304387 M. B. Ahmadi and M. Sadeghimehr, <a href="https://oam-rc.inoe.ro/download.php?idu=1158=52">Atom bond connectivity index of an infinite class NS1[n] of dendrimer nanostars</a>, Optoelectronics and Advanced Materials, 4(7):1040-1042 July 2010.
%H A304387 Ali Reza Ashrafi and Parisa Nikzad, <a href="http://www.chalcogen.ro/383_Ashrafi.pdf">Kekulé index and bounds of energy for nanostar dendrimers</a>, Digest J. of Nanomaterials and Biostructures, 4, No. 2, 2009, 383-388.
%H A304387 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A304387 From _Colin Barker_, May 18 2018: (Start)
%F A304387 G.f.: (22 - 17*x) / ((1 - x)*(1 - 2*x)).
%F A304387 a(n) = 3*a(n-1) - 2*a(n-2) for n>1.
%F A304387 (End)
%p A304387 seq(27*2^n-5, n = 0 .. 40);
%t A304387 27*2^Range[0,40]-5 (* or *) LinearRecurrence[{3,-2},{22,49},40] (* _Harvey P. Dale_, Jan 12 2019 *)
%o A304387 (PARI) a(n) = 27*2^n - 5; \\ _Altug Alkan_, May 13 2018
%o A304387 (PARI) Vec((22 - 17*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ _Colin Barker_, May 18 2018
%o A304387 (GAP) List([1..40],n->27*2^n-5); # _Muniru A Asiru_, May 13 2018
%Y A304387 Cf. A304386, A250653.
%K A304387 nonn,easy
%O A304387 0,1
%A A304387 _Emeric Deutsch_, May 13 2018
%E A304387 Offset changed by _N. J. A. Sloane_, May 13 2018