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A304169 a(n) = 16*3^n + 2^(n+1) - 26 (n>=1).

%I A304169 #18 May 13 2018 08:55:35
%S A304169 26,126,422,1302,3926,11766,35222,105462,315926,946806,2838422,
%T A304169 8511222,25525526,76560246,229648022,688878582,2066504726,6199252086,
%U A304169 18597232022,55790647542,167369845526,502105342326,1506307638422,4518906138102,13556684859926,40669987470966
%N A304169 a(n) = 16*3^n + 2^(n+1) - 26 (n>=1).
%C A304169 For n>=2, a(n) is the first Zagreb index of the Sierpinski Gasket Rhombus graph SR[n] (see the Antony Xavier et al. reference).
%C A304169 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 A304169 The M-polynomial of the Sierpinski Gasket Rhombus graph SR[n] is M(SR[n]; x,y) = 4*x^2*y^4 + 4*x^3*y^4 +2*x^3*y^6 + (2*3^n - 3*2^n - 4)*x^4*y^4 + (2^{n+1} - 4)*x^4*y^6 + (2^{n-1} - 2)*x^6*y^6.
%H A304169 Colin Barker, <a href="/A304169/b304169.txt">Table of n, a(n) for n = 1..1000</a>
%H A304169 D. Antony Xavier, M. Rosary, and Andrew Arokiaraj, <a href="https://www.ijmsc.com/index.php/ijmsc/article/view/261">Topological properties of Sierpinski Gasket Rhombus graphs</a>, International J. of Mathematics and Soft Computing, 4, No. 2, 2014, 95-104.
%H A304169 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 A304169 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6).
%F A304169 From _Colin Barker_, May 11 2018: (Start)
%F A304169 G.f.: 2*x*(13 - 15*x - 24*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)).
%F A304169 a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) for n>3.
%F A304169 (End)
%p A304169 seq(16*3^n+2^(n+1)-26, n = 1 .. 30);
%o A304169 (PARI) Vec(2*x*(13 - 15*x - 24*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)) + O(x^30)) \\ _Colin Barker_, May 11 2018
%Y A304169 Cf. A304170.
%K A304169 nonn,easy
%O A304169 1,1
%A A304169 _Emeric Deutsch_, May 11 2018