A386847 a(n) is the number of sets of distinct five-cuboid combinations that fill an n X n X n cube excluding combinations that contain strict cuboids.

0, 0, 1, 3, 10, 19, 30, 44, 64, 84, 100, 141, 150, 202, 218, 279, 282, 382, 365, 478, 470, 603, 568, 749, 690, 897, 840, 1066, 980, 1279, 1151, 1473, 1357, 1716, 1552, 1988, 1785, 2265, 2062, 2573, 2327, 2947, 2640, 3296, 3006, 3718, 3361, 4182, 3774, 4659, 4251

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 five triplets of the form (x,y,z) excluding x != y != z in any of the triplets.

Examples

			(4,4,4) triplet can be decomposed into sets of five triplets in 31 different ways and only the following three sets do not contain strict cuboids:
  {(1,1,1), (1,1,2), (1,1,4), (1,3,3), (3,4,4)},
  {(1,1,1), (1,1,2), (1,3,3), (1,4,4), (3,3,4)},
  {(1,1,3), (1,1,4), (1,3,3), (1,4,4), (2,4,4)}.
		

Crossrefs

Cf. A384479.

Extensions

a(16)-a(39) from Sean A. Irvine, Aug 06 2025

More terms from Jinyuan Wang, Aug 10 2025