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A304519
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a(n) = 72*2^n -56 (n>=1).
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2
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88, 232, 520, 1096, 2248, 4552, 9160, 18376, 36808, 73672, 147400, 294856, 589768, 1179592, 2359240, 4718536, 9437128, 18874312, 37748680, 75497416, 150994888, 301989832, 603979720, 1207959496, 2415919048, 4831838152, 9663676360, 19327352776, 38654705608, 77309411272, 154618822600, 309237645256, 618475290568
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OFFSET
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1,1
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COMMENTS
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a(n) is the second Zagreb index of the nanostar dendrimer NS2[n] from the Madanshekaf et al. reference.
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.
The M-polynomial of NS2[n] is M(NS2[n]; x,y) = 2*2^n *x*y^2 + (8*2^n - 5)*x^2*y^2 + (6*2^n - 6)*x^2*y^3.
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LINKS
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FORMULA
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G.f.: 8*x*(11 - 4*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(72*2^n-56, n = 1 .. 40);
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PROG
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(PARI) Vec(8*x*(11 - 4*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 15 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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