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a(n) = 192*2^n - 31 (n>=1).
2

%I #21 May 16 2018 13:19:18

%S 353,737,1505,3041,6113,12257,24545,49121,98273,196577,393185,786401,

%T 1572833,3145697,6291425,12582881,25165793,50331617,100663265,

%U 201326561,402653153,805306337,1610612705,3221225441,6442450913,12884901857,25769803745,51539607521

%N a(n) = 192*2^n - 31 (n>=1).

%C a(n) is the second 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 second Zagreb index of a simple connected graph is the sum of the degree products 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="/A304385/b304385.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.: x*(353 - 322*x) / ((1 - x)*(1 - 2*x)).

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

%F (End)

%p seq(192*2^n-31, n = 1 .. 40);

%o (GAP) List([1..40],n->192*2^n-31); # _Muniru A Asiru_, May 13 2018

%o (PARI) Vec(x*(353 - 322*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ _Colin Barker_, May 14 2018

%Y Cf. A304384.

%K nonn,easy

%O 1,1

%A _Emeric Deutsch_, May 13 2018