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

1,4

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.

Links

Table of n, a(n) for n=1..11.

Example

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).

Sequence in context: A258375 A306953 A302573 * A251933 A061170 A125114

Adjacent sequences: A385244 A385245 A385246 * A385248 A385249 A385250

Keyword

nonn,more

Author

Sean A. Irvine and Janaka Rodrigo, Jul 28 2025

Status

approved