%I
%S 0,0,0,1,0,0,4,10,19,31,44
%N Magic deficiency of the complete graph K_n on n vertices.
%D W. D. Wallis. Magic Graphs. Birkhauser, (2001). Section 2.10.
%H A. Kotzig and A. Rosa, <a href="http://dx.doi.org/10.4153/CMB19700841">Magic Valuations of Finite Graphs</a>, Canad. Math. Bull. v.13 (1970), pp. 451461.
%H J. P. McSorley and J. A. Trono, <a href="https://doi.org/10.1016/j.disc.2009.07.021">On kminimum and mminimum EdgeMagic Injections of Graphs</a>, Discrete Mathematics, Volume 310, Issue 1, 6 January 2010, Pages 5669.
%e 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.
%e Hence the magic deficiency of K_4 is a(4)=1110=1.
%Y See sequence A152682. The nth term of the magic deficiency sequence equals the nth term of sequence A152682 minus "n+{n choose 2}".
%Y (The number "n+{n choose 2}" is the total number of vertices and edges in K_n.)
%Y See also sequence A129413 which concerns the smallest value of the magic sum of an edgemagic injection of K_n.
%K nonn,more
%O 1,7
%A _John P. McSorley_, Dec 15 2008
