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%I #18 May 30 2018 09:11:58
%S 65,229,557,1213,2525,5149,10397,20893,41885,83869,167837,335773,
%T 671645,1343389,2686877,5373853,10747805,21495709,42991517,85983133,
%U 171966365,343932829,687865757,1375731613,2751463325,5502926749,11005853597,22011707293,44023414685,88046829469,176093659037
%N a(n) = 164*2^n - 99.
%C a(n) (n>=0) is the second Zagreb index of the nanostar dendrimer G(n), defined pictorially in the Darafsheh et al. reference (see Fig. 1, where G(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 G(n) is M(G(n);x,y) = 8*2^n*x^2*y^2 + (16*2^n - 12)*x^2*y^3 + (4*2^n - 3)*x^3*y^3.
%D M. R. Darafsheh, M. H. Khalifeh, Calculation of the Wiener, Szeged, and PI indices of a certain nanostar dendrimer, Ars Comb., 100, 2011, 289-298.
%H Muniru A Asiru, <a href="/A305157/b305157.txt">Table of n, a(n) for n = 0..700</a>
%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 30 2018: (Start)
%F G.f.: (65 + 34*x) / ((1 - x)*(1 - 2*x)).
%F a(n) = 3*a(n-1) - 2*a(n-2) for n>1.
%F (End)
%p seq(164*2^n-99, n = 0 .. 40);
%o (GAP) List([0..40], n->164*2^n-99); # _Muniru A Asiru_, May 30 2018
%o (PARI) Vec((65 + 34*x) / ((1 - x)*(1 - 2*x)) + O(x^30)) \\ _Colin Barker_, May 30 2018
%Y Cf. A226264, A305155, A305156.
%K nonn,easy
%O 0,1
%A _Emeric Deutsch_, May 28 2018