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A304608
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a(n) = 288*2^n + 178 (n >= 1).
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4
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754, 1330, 2482, 4786, 9394, 18610, 37042, 73906, 147634, 295090, 590002, 1179826, 2359474, 4718770, 9437362, 18874546, 37748914, 75497650, 150995122, 301990066, 603979954, 1207959730, 2415919282, 4831838386, 9663676594, 19327353010, 38654705842, 77309411506, 154618822834, 309237645490, 618475290802
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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 G[n] from the Ashrafi 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 G[n] is M(G[n]; x,y) = 4*x*y^4 + (18*2^n + 21)*x^2*y^2 + (36*2^n - 9)*x^2*y^3 + 3*x^2*y^4 + 9*x^3*y^4.
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LINKS
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FORMULA
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G.f.: 2*x*(377 - 466*x)/(1 - 3*x + 2*x^2).
a(n) = 3*a(n - 1) - 2*a(n - 2) for n > 2. (End)
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MAPLE
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seq(288*2^n+178, n = 1 .. 40);
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MATHEMATICA
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CoefficientList[Series[2 (377 - 466 x)/(1 - 3 x + 2 x^2), {x, 0, 30}], x] (* or *)
LinearRecurrence[{3, -2}, {754, 1330}, 31] (* or *)
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PROG
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(PARI) a(n) = 288*2^n + 178; \\ Altug Alkan, May 15 2018
(PARI) Vec(2*x*(377 - 466*x)/(1 - 3*x + 2*x^2) + O(x^40)) \\ Colin Barker, May 23 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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