

A152946


Magic deficiency of the complete graph K_n on n vertices.


0



0, 0, 0, 1, 0, 0, 4, 10, 19, 31, 44
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OFFSET

1,7


REFERENCES

W. D. Wallis. Magic Graphs. Birkhauser, (2001). Section 2.10.


LINKS

Table of n, a(n) for n=1..11.
A. Kotzig and A. Rosa, Magic Valuations of Finite Graphs, Canad. Math. Bull. v.13 (1970), pp. 451461.
J. P. McSorley and J. A. Trono, On kminimum and mminimum EdgeMagic Injections of Graphs, Discrete Mathematics, Volume 310, Issue 1, 6 January 2010, Pages 5669.


EXAMPLE

a(4)=1 because when forming an edgemagic 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 edgemagic 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)=1110=1.


CROSSREFS

See sequence A152682. The nth term of the magic deficiency sequence equals the nth 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 edgemagic injection of K_n.
Sequence in context: A008038 A301248 A160425 * A162505 A025720 A022793
Adjacent sequences: A152943 A152944 A152945 * A152947 A152948 A152949


KEYWORD

nonn,more


AUTHOR

John P. McSorley, Dec 15 2008


STATUS

approved



