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A181617
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Molecular topological indices of the complete graph K_n.
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7
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0, 4, 24, 72, 160, 300, 504, 784, 1152, 1620, 2200, 2904, 3744, 4732, 5880, 7200, 8704, 10404, 12312, 14440, 16800, 19404, 22264, 25392, 28800, 32500, 36504, 40824, 45472, 50460, 55800, 61504, 67584, 74052, 80920, 88200, 95904, 104044, 112632, 121680, 131200
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OFFSET
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1,2
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COMMENTS
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a(n) = the area of a trapezoid with vertices at (n-1,n), (n,n-1), ((n-1)^2,n^2), and (n^2,(n-1)^2). - J. M. Bergot, Mar 23 2014
For n > 3, also the detour index of the (n-1)-helm graph. - Eric W. Weisstein, Dec 16 2017
a(n-3) is the maximum sigma irregularity over all maximal 2-degenerate graphs with n vertices. The extremal graphs are 2-stars (K_2 joined to n-2 independent vertices). (The sigma irregularity of a graph is the sum of the squares of the differences between the degrees over all edges of the graph.) - Allan Bickle, Jun 14 2023
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LINKS
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Eric Weisstein's World of Mathematics, Helm Graph.
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FORMULA
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a(n) = 2*n*(n-1)^2.
Sum_{n>=2} 1/a(n) = Pi^2/12 - 1/2.
Sum_{n>=2} (-1)^n/a(n) = Pi^2/24 - log(2) + 1/2. (End)
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MATHEMATICA
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CoefficientList[Series[4 x (1 + 2 x)/(1 - x)^4, {x, 0, 50}], x] (* Vincenzo Librandi, Mar 24 2014 *)
LinearRecurrence[{4, -6, 4, -1}, {0, 4, 24, 72}, 50] (* Harvey P. Dale, Jun 16 2016 *)
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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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EXTENSIONS
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STATUS
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approved
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