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A304384
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a(n) = 168*2^n - 26 (n>=1).
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2
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310, 646, 1318, 2662, 5350, 10726, 21478, 42982, 85990, 172006, 344038, 688102, 1376230, 2752486, 5504998, 11010022, 22020070, 44040166, 88080358, 176160742, 352321510, 704643046, 1409286118, 2818572262, 5637144550, 11274289126, 22548578278, 45097156582, 90194313190
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OFFSET
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1,1
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COMMENTS
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a(n) is the first Zagreb index of the molecular graph NS2[n], defined pictorially in the Ashrafi et al. reference (Fig. 2, where NS2[2] is shown).
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.
The M-polynomial of NS2[n] is M(NS2[n]; x,y) = (12*2^n + 2)x^2*y^2 + (24*2^n - 8)x^2*y^3 + x^3*y^3.
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LINKS
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FORMULA
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G.f.: 2*x*(155 - 142*x) / ((1 - x)*(1 - 2*x)).
a(n) = 3*a(n-1) - 2*a(n-2) for n>2.
(End)
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MAPLE
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seq(168*2^n-26, n = 1 .. 40);
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PROG
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(PARI) Vec(2*x*(155 - 142*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 14 2018
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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