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A304838 a(n) = 1944*n^2 - 5016*n + 3138 (n >= 1).

%I A304838 #23 Dec 02 2018 16:57:23
%S A304838 66,882,5586,14178,26658,43026,63282,87426,115458,147378,183186,
%T A304838 222882,266466,313938,365298,420546,479682,542706,609618,680418,
%U A304838 755106,833682,916146,1002498,1092738,1186866,1284882,1386786,1492578,1602258,1715826,1833282,1954626,2079858
%N A304838 a(n) = 1944*n^2 - 5016*n + 3138 (n >= 1).
%C A304838 a(n) is the second Zagreb index of the hex derived network HDN1(n) from the Manuel et al. reference (see HDN1(4) in Fig. 8).
%C A304838 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 A304838 The M-polynomial of HDN1(n) is M(HDN1(n);x,y) = 12*x^3*y^5 + (18*(n-2))*x^3*y^7 + (6*(3*n^2-9*n+7))*x^3*y^12 + 12*x^5*y^7 + 6*x^5*y^12 + (6*(n-3))*x^7*y^7 + (12*(n-2))*x^7*y^12 + (3*(n-2)*(3*n-5)*x^12*y^12.
%H A304838 Colin Barker, <a href="/A304838/b304838.txt">Table of n, a(n) for n = 1..1000</a>
%H A304838 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 A304838 P. Manuel, R. Bharati, I. Rajasingh, and Chris Monica M, <a href="https://doi.org/10.1016/j.jda.2006.09.002">On minimum metric dimension of honeycomb networks</a>, J. Discrete Algorithms, 6, 2008, 20-27.
%H A304838 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A304838 G.f.: 6*x*(11 + 114*x + 523*x^2)/(1 - x)^3. - _Bruno Berselli_, May 22 2018
%p A304838 seq(3138 - 5016*n + 1944*n^2, n = 1 .. 45);
%t A304838 Table[1944 n^2 - 5016 n + 3138, {n, 1, 40}] (* _Bruno Berselli_, May 22 2018 *)
%t A304838 LinearRecurrence[{3,-3,1},{66,882,5586},40] (* _Harvey P. Dale_, Dec 02 2018 *)
%o A304838 (GAP) List([1..50], n->1944*n^2-5016*n+3138); # _Muniru A Asiru_, May 22 2018
%o A304838 (PARI) Vec(6*x*(11 + 114*x + 523*x^2)/(1 - x)^3 + O(x^40)) \\ _Colin Barker_, May 23 2018
%Y A304838 Cf. A082040, A304836, A304837.
%K A304838 nonn,easy
%O A304838 1,1
%A A304838 _Emeric Deutsch_, May 21 2018