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A067707
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a(n) = 3*n^2 + 12*n.
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10
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15, 36, 63, 96, 135, 180, 231, 288, 351, 420, 495, 576, 663, 756, 855, 960, 1071, 1188, 1311, 1440, 1575, 1716, 1863, 2016, 2175, 2340, 2511, 2688, 2871, 3060, 3255, 3456, 3663, 3876, 4095, 4320, 4551, 4788, 5031, 5280, 5535, 5796, 6063, 6336, 6615, 6900
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OFFSET
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1,1
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COMMENTS
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Numbers k such that 12*(12 + k) is a perfect square.
a(n) is the second Zagreb index of the gear graph g[n]. 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 gear graph g[n] is defined as a wheel graph with n+1 vertices with a vertex added between each pair of adjacent vertices of the outer cycle. - Emeric Deutsch, Nov 09 2016
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LINKS
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Eric Weisstein's World of Mathematics, Gear Graph.
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FORMULA
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Sum_{n>=1} 1/a(n) = 25/144.
Sum_{n>=1} (-1)^(n+1)/a(n) = 7/144. (End)
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MATHEMATICA
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Select[ Range[10000], IntegerQ[ Sqrt[ 12(12 + # )]] & ]
CoefficientList[Series[3*(5-3*x)/(1-x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 07 2012 *)
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PROG
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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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