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%I #18 Sep 13 2013 21:00:37
%S 1,1,1,1,2,1,1,3,2,1,1,4,4,2,1,1,5,7,5,2,1,1,6,12,12,6,2,1,1,7,18,24,
%T 16,7,2,1,1,8,26,46,42,23,8,2,1,1,9,35,83,101,73,29,9,2,1
%N Maximum label within a minimal labeling of k >= 0 identical n-sided dice (n >= 1) yielding the most possible sums; square array A(n,k), read by antidiagonals.
%H The <a href="http://domino.research.ibm.com/Comm/wwwr_ponder.nsf/Challenges/July2013.html">IBM Ponder This July 2013</a> challenge asks for A(8,3).
%e Three tetrahedra labeled (1, 2, 8, 12) yield the 20 possible sums 3, 4, 5, 6, 10, 11, 12, 14, 15, 16, 17, 18, 21, 22, 24, 25, 26, 28, 32, 36. No more sums can be obtained by different labelings, and no labeling with labels < 12 yields 20 possible sums. Therefore A(4,3) = 12.
%e Square array A(n,k) begins:
%e 1, 1, 1, 1, 1, 1, 1, 1, ...
%e 1, 2, 2, 2, 2, 2, 2, ...
%e 1, 3, 4, 5, 6, 7, ...
%e 1, 4, 7, 12, 16, ...
%e 1, 5, 12, 24, ...
%e 1, 6, 18, ...
%e 1, 7, ...
%e 1, ...
%Y Cf. A227589, A227590, A227358.
%K nonn,tabl,more
%O 1,5
%A _Jens Voß_, Jul 17 2013
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