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%I #25 Jul 31 2019 18:52:46
%S 94,208,322,436,550,664,778,892,1006,1120,1234,1348,1462,1576,1690,
%T 1804,1918,2032,2146,2260,2374,2488,2602,2716,2830,2944,3058,3172,
%U 3286,3400,3514,3628,3742,3856,3970,4084,4198,4312,4426,4540
%N a(n) = 114*n - 20.
%C a(n) is the first Zagreb index of the polymer B[n,1], defined pictorially in the Bodroža-Pantić et al. reference (Fig. 4).
%C a(n) is the first Zagreb index of the polymer B[n,2], defined pictorially in the Bodroža-Pantić et al. reference (Fig. 4).
%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 B[n,1] is M(B[n,1]; x,y) = 2*(2*n+1)*x^2*y^2 + 4*(n+1)*x^2*y^3 + (13*n-8)*x^3*y^3.
%C The M-polynomial of B[n,2] is M(B[n,1]; x,y) = 2*(n+2)*x^2*y^2 + 8*n*x^2*y^3 + (11*n-6)*x^3*y^3.
%H Colin Barker, <a href="/A304609/b304609.txt">Table of n, a(n) for n = 1..1000</a>
%H O. Bodroža-Pantić, I. Gutman, and S. J. Cyvin, <a href="https://www.researchgate.net/publication/330778512_Algebraic_structure_count_of_some_non-benzenoid_conjugated_polymers">Algebraic structure count of some non-benzenoid conjugated polymers</a>, ACH - Models in Chemistry, 133 (1-2), 27-41, 1996.
%H E. Deutsch and Sandi Klavžar, <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 (2,-1).
%F From _Colin Barker_, May 17 2018: (Start)
%F G.f.: 2*x*(47 + 10*x) / (1 - x)^2.
%F a(n) = 2*a(n-1) - a(n-2) for n>2.
%F (End)
%p seq(114*n-20, n = 1 .. 40);
%o (PARI) a(n) = 114*n - 20; \\ _Altug Alkan_, May 16 2018
%o (PARI) Vec(2*x*(47 + 10*x) / (1 - x)^2 + O(x^40)) \\ _Colin Barker_, May 17 2018
%o (GAP) List([1..80], n->114*n-20); # _Muniru A Asiru_, May 17 2018
%Y Cf. A304610, A304611.
%K nonn,easy
%O 1,1
%A _Emeric Deutsch_, May 16 2018
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