A386846 -id:A386846 - cp's OEIS frontend

A386848 Array read by descending antidiagonals:T(n,k) is the number of ways to partition n X n X n cube into k noncongruent cuboids excluding strict cuboids.

1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 2, 0, 2, 1, 0, 0, 1, 3, 0, 2, 1, 0, 0, 1, 3, 4, 1, 3, 1, 0, 0, 0, 1, 10, 6, 1, 3, 1, 0, 0, 0, 6, 9, 19, 6, 2, 4, 1, 0, 0, 0, 5, 34, 24, 30, 9, 3, 4, 1, 0, 0, 0, 0, 78, 37, 47, 44, 8, 4, 5, 1, 0, 0, 0, 0, 93

Offset: 1

Janaka Rodrigo, Aug 05 2025

A strict cuboid is a cuboid with all dimensions different to each other.

The partitions here must be valid packings 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.

			1    0    0    0    0
1    0    0    0    0
1    1    0    2    1
1    1    0    3    3
1    2    0    4   10
1    2    1    6   19
1    3    1    6   30
1    3    2    9   44
1    4    3    8   64
1    4    4    13  84

Sean A. Irvine, Table of n, a(n) for n = 1..140

Cf. A386296.

Columns: A004526(k=2), A211540(k=3), A386846(k=4), A386847(k=5).

T(n,1) = 1,

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

More terms from Sean A. Irvine, Aug 05 2025

cp's OEIS Frontend

A386848 Array read by descending antidiagonals:T(n,k) is the number of ways to partition n X n X n cube into k noncongruent cuboids excluding strict cuboids.

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