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A152946
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Magic deficiency of the complete graph K_n on n vertices.
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0
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0, 0, 0, 1, 0, 0, 4, 10, 19, 31, 44
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listen;
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OFFSET
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1,7
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REFERENCES
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W. D. Wallis. Magic Graphs. Birkhäuser, (2001). Section 2.10.
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LINKS
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EXAMPLE
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a(4)=1 because when forming an edge-magic injection of K_4 we must use at least the first 10 natural numbers {1,2,...,10} since K_4 has a total of 10 vertices and edges. However, this is not possible. But there is an edge-magic injection of K_4 using the set {1,2,...,11}\{4}, with largest label 11.
Hence the magic deficiency of K_4 is a(4)=11-10=1.
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CROSSREFS
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See sequence A152682. The n-th term of the magic deficiency sequence equals the n-th term of sequence A152682 minus "n+{n choose 2}".
(The number "n+{n choose 2}" is the total number of vertices and edges in K_n.)
See also sequence A129413 which concerns the smallest value of the magic sum of an edge-magic injection of K_n.
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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