A386779 Array read by descending antidiagonals: T(n,k) is the number of ways to partition an n X n X n cube into k noncongruent cuboids excluding cube-shaped parts.

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 2, 3, 2, 0, 0, 0, 1, 10, 8, 2, 0, 0, 0, 0, 21, 43, 11, 3, 0, 0, 0, 0, 37, 179, 81, 19, 3, 0, 0, 0, 0, 38, 644, 513, 177, 23, 4, 0, 0, 0, 0, 15, 2068, 3024, 1471, 260, 35, 4, 0, 0, 0, 0, 4, 4995, 17489, 11776, 2736, 458, 40, 5

Offset

1,13

Comments

The partition here must be valid packing of the n X n X n cube, hence T(n,k) is generally less than the number of partitions of n^3 into distinct cuboids (x,y,z) with 1 <= x,y,z <= n and volume x*y*z excluding x=y=z.

Links

Sean A. Irvine, Table of n, a(n) for n = 1..97

Formula

T(n,1) = 0

T(n,k) = 0 for k > n^3

T(n,k) = A381847(n) for k = 3.

Example

Array begins
  0    0    0    0     0
  0    0    0    0     0
  0    1    2    2     1
  0    1    3   10    21
  0    2    8   43   179
  0    2   11   81   513
  0    3   19  177  1471
  0    3   23  260  2736
  0    4   35  458  5713
  0    4   40  605  8881

Crossrefs

Cf. columns: A004526 (k=2), A381847 (k=3), A386756 (k=4), A386757 (k=5).

Sequence in context: A339829 A177517 A227819 * A064287 A196389 A128206

Adjacent sequences: A386776 A386777 A386778 * A386780 A386781 A386782

Keyword

tabl,nonn

Author

Janaka Rodrigo, Aug 02 2025

Extensions

More terms from Sean A. Irvine, Aug 03 2025

Status

approved