A386757 -id:A386757 - cp's OEIS frontend

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

Janaka Rodrigo, Aug 02 2025

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.

			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

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

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

T(n,1) = 0
T(n,k) = 0 for k > n^3
T(n,k) = A381847(n) for k = 3.

More terms from Sean A. Irvine, Aug 03 2025

cp's OEIS Frontend

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.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

Extensions