A386756 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 cube-shaped cuboids.

0, 0, 2, 10, 43, 81, 177, 260, 458, 605, 931, 1169, 1656, 1995, 2687, 3145, 4063, 4674, 5850, 6617, 8102, 9044, 10852, 12008, 14172, 15540, 18116, 19714, 22711, 24585, 28035, 30176, 34142, 36569, 41053, 43817, 48852, 51939, 57593, 61021, 67291, 71118, 78036, 82241, 89882

Offset: 1

Author

Janaka Rodrigo, Aug 01 2025

Keywords

• nonn

Comments

Alternatively, a(n) is the number of ways to decompose a (n,n,n) triplet into sets of four unordered triplets of the form (x,y,z) without having x=y=z in any of the triplets.

Examples

			There are 12 sets of distinct four-cuboid combinations filling 4 X 4 X 4 cube according to A384311(4), only two combinations containing cubes listed below,
   {(1,1,1), (1,1,3), (1,3,4), (3,4,4)},
   {(1,3,3), (3,3,3), (1,3,4), (1,4,4)}.
Therefore, a(4) = 12-2 = 10.
		

Crossrefs

Cf. A384311.