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%I #21 May 13 2018 08:51:06
%S 108,312,720,1536,3168,6432,12960,26016,52128,104352,208800,417696,
%T 835488,1671072,3342240,6684576,13369248,26738592,53477280,106954656,
%U 213909408,427818912,855637920,1711275936,3422551968,6845104032,13690208160,27380416416,54760832928,109521665952,219043332000,438086664096
%N a(n) = 102*2^n - 96 (n>=1).
%C a(n) is the second Zagreb index of the triangulane T(n), defined pictorially in the Khalifeh et al. reference.
%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 the triangulane T[n] is M(T[n]; x,y) = 3*2^{n-1}*x^2*y^2 + 3*2^n*x^2*y^4 + (9*2^{n-1} - 6)*x^4*y^4.
%H Colin Barker, <a href="/A304377/b304377.txt">Table of n, a(n) for n = 1..1000</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 M. H. Khalifeh, H. Yousefi-Azari, A. R. Ashrafi, <a href="http://nopr.niscair.res.in/handle/123456789/2215">Computing Wiener and Kirchhoff indices of a triangulane</a>, Indian J. Chemistry, 47A, 2008, 1503-1507.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Triangulane">Triangulane</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F From _Colin Barker_, May 13 2018: (Start)
%F G.f.: 12*x*(9 - x) / ((1 - x)*(1 - 2*x)).
%F a(n) = 3*a(n-1) - 2*a(n-2) for n>2.
%F (End)
%p seq(102*2^n - 96, n=1..40);
%o (PARI) Vec(12*x*(9 - x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ _Colin Barker_, May 13 2018
%Y Cf. A304376.
%K nonn,easy
%O 1,1
%A _Emeric Deutsch_, May 12 2018
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