A227588 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.

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, 16, 7, 2, 1, 1, 8, 26, 46, 42, 23, 8, 2, 1, 1, 9, 35, 83, 101, 73, 29, 9, 2, 1

Offset: 1

Author

Jens Voß, Jul 17 2013

Keywords

• nonn
• tabl
• more

Examples

			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.
Square array A(n,k) begins:
  1, 1,  1,  1,  1, 1, 1, 1, ...
  1, 2,  2,  2,  2, 2, 2, ...
  1, 3,  4,  5,  6, 7, ...
  1, 4,  7, 12, 16, ...
  1, 5, 12, 24, ...
  1, 6, 18, ...
  1, 7, ...
  1, ...
		

Links

• The IBM Ponder This July 2013 challenge asks for A(8,3).

Crossrefs

Cf. A227589, A227590, A227358.