A304384 - OEIS

%I #19 May 16 2018 13:19:14

%S 310,646,1318,2662,5350,10726,21478,42982,85990,172006,344038,688102,

%T 1376230,2752486,5504998,11010022,22020070,44040166,88080358,

%U 176160742,352321510,704643046,1409286118,2818572262,5637144550,11274289126,22548578278,45097156582,90194313190

%N a(n) = 168*2^n - 26 (n>=1).

%C a(n) is the first Zagreb index of the molecular graph NS2[n], defined pictorially in the Ashrafi et al. reference (Fig. 2, where NS2[2] is shown).

%C 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 The M-polynomial of NS2[n] is M(NS2[n]; x,y) = (12*2^n + 2)x^2*y^2 + (24*2^n - 8)x^2*y^3 + x^3*y^3.

%H Colin Barker, <a href="/A304384/b304384.txt">Table of n, a(n) for n = 1..1000</a>

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

%F From _Colin Barker_, May 14 2018: (Start)

%F G.f.: 2*x*(155 - 142*x) / ((1 - x)*(1 - 2*x)).

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

%F (End)

%p seq(168*2^n-26, n = 1 .. 40);

%o (GAP) List([1..40],n->168*2^n-26); # _Muniru A Asiru_, May 13 2018

%o (PARI) Vec(2*x*(155 - 142*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ _Colin Barker_, May 14 2018

%Y Cf. A304385.

%K nonn,easy

%O 1,1

%A _Emeric Deutsch_, May 13 2018