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a(n) = 60*2^n - 48 (n>=1).
2

%I #14 May 13 2018 08:51:03

%S 72,192,432,912,1872,3792,7632,15312,30672,61392,122832,245712,491472,

%T 982992,1966032,3932112,7864272,15728592,31457232,62914512,125829072,

%U 251658192,503316432,1006632912,2013265872,4026531792,8053063632,16106127312,32212254672,64424509392,128849018832

%N a(n) = 60*2^n - 48 (n>=1).

%C a(n) is the first Zagreb index of the triangulane T[n], defined pictorially in the Khalifeh et al. reference.

%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 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="/A304376/b304376.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 <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.: 24*x*(3 - x) / ((1 - x)*(1 - 2*x)).

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

%F (End)

%p seq(60*2^n - 48, n=1..40);

%o (PARI) Vec(24*x*(3 - x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ _Colin Barker_, May 13 2018

%Y Cf. A304377.

%K nonn,easy

%O 1,1

%A _Emeric Deutsch_, May 12 2018