cp's OEIS Frontend

A304389 a(n) = 126*2^n - 22 (n>=1).

%I A304389 #23 May 22 2018 09:48:19
%S A304389 230,482,986,1994,4010,8042,16106,32234,64490,129002,258026,516074,
%T A304389 1032170,2064362,4128746,8257514,16515050,33030122,66060266,132120554,
%U A304389 264241130,528482282,1056964586,2113929194,4227858410,8455716842,16911433706,33822867434,67645734890,135291469802,270582939626,541165879274
%N A304389 a(n) = 126*2^n - 22 (n>=1).
%C A304389 a(n) is the first Zagreb index of 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).
%C A304389 The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternatively, it is the sum of the degree sums d(i) + d(j) over all edges ij of the graph.
%C A304389 The M-polynomial of NS1[n] is M(NS1[n]; x,y) = xy^4 + (9*2^n + 3)x^2*y^2 + (18*2^n - 12)x^2*y^3 + 3x^3*y^4 .
%H A304389 Colin Barker, <a href="/A304389/b304389.txt">Table of n, a(n) for n = 1..1000</a>
%H A304389 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 A304389 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 A304389 E. Deutsch and Sandi Klavzar, <a href="http://dx.doi.org/10.22052/ijmc.2015.10106">M-polynomial and degree-based topological indices</a>, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
%H A304389 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A304389 From _Colin Barker_, May 18 2018: (Start)
%F A304389 G.f.: 2*x*(115 - 104*x) / ((1 - x)*(1 - 2*x)).
%F A304389 a(n) = 3*a(n-1) - 2*a(n-2) for n>2.
%F A304389 (End)
%p A304389 seq(126*2^n-22, n = 1 .. 40);
%o A304389 (PARI) a(n) = 126*2^n - 22; \\ _Altug Alkan_, May 13 2018
%o A304389 (PARI) Vec(2*x*(115 - 104*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ _Colin Barker_, May 18 2018
%o A304389 (GAP) List([1..40],n->126*2^n-22); # _Muniru A Asiru_, May 13 2018
%Y A304389 Cf. A304386, A304387, A304388.
%K A304389 nonn,easy
%O A304389 1,1
%A A304389 _Emeric Deutsch_, May 13 2018