A386884 a(n) is the number of distinct four-cuboid combinations that fill an n X n X n cube using only strict cuboids.

0, 0, 0, 0, 1, 2, 9, 12, 30, 36, 70, 80, 135, 150, 231, 252, 364, 392, 540, 576, 765, 810, 1045, 1100, 1386, 1452, 1794, 1872, 2275, 2366, 2835, 2940, 3480, 3600, 4216, 4352, 5049, 5202, 5985, 6156, 7030, 7220, 8190, 8400, 9471, 9702, 10879, 11132, 12420

Offset: 1

Author

Janaka Rodrigo, Aug 06 2025

Keywords

• nonn

Comments

A strict cuboid is a cuboid with all three dimensions different.

Alternatively a(n) is the number of ways to decompose triplet (n,n,n) into sets of distinct four unordered triplets of the form (x,y,z) with x != y != z for each of the four triplets.

Examples

			As described in A384311 there are 85 sets of distinct four-cuboid combinations filling 6 X 6 X 6 cube and only two of those have all four triplets with different elements, those are;
   {(1,2,6), (1,4,6), (2,5,6), (4,5,6)},
   {(1,3,6), (2,3,6), (3,4,6), (3,5,6)}.
Therefore a(6) = 2.
		

Crossrefs

Cf. A384311.

Extensions

More terms from Sean A. Irvine, Aug 06 2025