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

1,5

Links

Table of n, a(n) for n=1..55.

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

Example

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, ...

Crossrefs

Cf. A227589, A227590, A227358.

Sequence in context: A052509 A172119 A228125 * A093628 A186807 A114282

Adjacent sequences: A227585 A227586 A227587 * A227589 A227590 A227591

Keyword

nonn,tabl,more

Author

Jens Voß, Jul 17 2013

Status

approved