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a(n) = 155*n - 38.

2

`%I #17 Jul 31 2019 18:11:57
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`%S 117,272,427,582,737,892,1047,1202,1357,1512,1667,1822,1977,2132,2287,
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`%T 2442,2597,2752,2907,3062,3217,3372,3527,3682,3837,3992,4147,4302,
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`%U 4457,4612,4767,4922,5077,5232,5387,5542,5697,5852,6007,6162,6317,6472,6627,6782,6937,7092,7247,7402,7557,7712
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`%N a(n) = 155*n - 38.
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`%C a(n) is the second Zagreb index of the polymer B(n,2), defined pictorially in the Bodroza-Pantic et al. reference (Fig. 4).
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`%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.
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`%C The M-polynomial of B[n,2] is M(B[n,2]; x,y) = 2*(n+2)*x^2*y^2 + 8*n*x^2*y^3 + (11*n-6)*x^3*y^3.
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`%H Colin Barker, <a href="/A304611/b304611.txt">Table of n, a(n) for n = 1..1000</a>
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`%H O. Bodroza-Pantic, 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.
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`%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.
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`%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1)
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`%F From _Colin Barker_, May 29 2018: (Start)
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`%F G.f.: x*(117 + 38*x) / (1 - x)^2.
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`%F a(n) = 2*a(n-1) - a(n-2) for n>2.
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`%F (End)
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`%p seq(155*n-38, n = 1 .. 50);
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`%o (PARI) Vec(x*(117 + 38*x) / (1 - x)^2 + O(x^50)) \\ _Colin Barker_, May 29 2018
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`%Y Cf. A304609.
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`%K nonn,easy
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`%O 1,1
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`%A _Emeric Deutsch_, May 24 2018
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