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A304385
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a(n) = 192*2^n - 31 (n>=1).
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2
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353, 737, 1505, 3041, 6113, 12257, 24545, 49121, 98273, 196577, 393185, 786401, 1572833, 3145697, 6291425, 12582881, 25165793, 50331617, 100663265, 201326561, 402653153, 805306337, 1610612705, 3221225441, 6442450913, 12884901857, 25769803745, 51539607521
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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 molecular graph NS2[n], defined pictorially in the Ashrafi et al. reference (Fig. 2, where NS2[2] is shown).
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) = (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.: x*(353 - 322*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(192*2^n-31, n = 1 .. 40);
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PROG
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(PARI) Vec(x*(353 - 322*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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