A386846 a(n) is the number of sets of distinct four-cuboid combinations that fill an n X n X n cube excluding combinations that contain strict cuboids.

0, 0, 2, 3, 4, 6, 6, 9, 8, 13, 11, 17, 15, 23, 20, 30, 27, 39, 36, 50, 47, 64, 61, 80, 78, 100, 98, 123, 122, 150, 150, 181, 182, 217, 219, 257, 261, 303, 308, 354, 361, 411, 420, 474, 485, 544, 557, 620, 636, 704, 722, 795, 816, 894, 918, 1001, 1028, 1117

Offset: 1

Author

Janaka Rodrigo, Aug 05 2025

Keywords

• nonn

Comments

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

Alternatively a(n) is number of ways to decompose (n,n,n) triplet into sets of distinct unordered geometrically feasible four triplets of the form (x,y,z) excluding x != y != z in any of the triplets.

Examples

			(5,5,5) triplet can be decomposed into sets of four triplets in 47 different ways and only the following 4 sets do not contain strict cuboids.
{(5,5,1), (5,4,4), (4,1,1), (1,4,4)},
{(5,5,3), (5,2,2), (3,3,2), (2,2,3)},
{(5,5,2), (3,3,5), (2,2,3), (3,3,2)},
{(4,1,1), (5,1,1), (1,4,4), (4,5,5)}.
		

Crossrefs

Cf. A384311.

Extensions

More terms from Sean A. Irvine, Aug 06 2025