A385247 a(n) is the number of ways to partition n X n X n cube into 6 noncongruent cuboids.

0, 0, 1, 70, 846, 3508, 12960, 30064, 74164, 134745, 266396

Offset: 1

Author

Sean A. Irvine and Janaka Rodrigo, Jul 28 2025

Keywords

• nonn
• more

Comments

A386296 is the main sequence for this topic.

Alternatively a(n) is the number of distinct six-cuboid combinations filling an n X n X n cube.

Examples

			Let the elements x,y and z of the unordered triplet (x,y,z) be the dimensions of a cuboid of the set of distinct six-cuboid combinations. One of the sets of six distinct unordered triplets of a(4) representing a six-cuboid combinations filling 4 X 4 X 4 cube is,
{(3,4,4),(1,2,3),(1,2,2),(1,1,3),(1,1,2),(1,1,1)}.
		

Crossrefs

Column 6 of A386296.

Cf. A381847 (3 cuboids), A384311 (4 cuboids), A384479 (5 cuboids).