A386902 a(n) is the number of distinct five-cuboid combinations that fill an n X n X n with only strict cuboids.

0, 0, 0, 0, 0, 18, 74, 193, 491, 857, 1695, 2503, 4321, 5836, 9200, 11715, 17284, 21256, 29805, 35589, 48156, 56260, 73766, 84860, 108495, 123080, 154298, 172998, 213045, 236895, 287260, 316743, 379465, 415456, 491930, 535713, 627879, 680052, 790401, 851914, 982130

Offset: 1

Author

Janaka Rodrigo, Aug 07 2025

Keywords

• nonn
• changed

Comments

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

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

Examples

			(6,6,6) triplet can be decomposed into set of five triplets in 560 different ways and only 18 of those formed by only strict cuboids. Three of those sets are given below:
   {(1,2,3), (1,3,4), (2,3,6), (3,4,6), (3,5,6)},
   {(1,2,6), (1,4,6), (2,4,6), (2,5,6), (3,4,6)},
   {(1,3,4), (1,3,6), (2,3,5), (2,3,6), (4,5,6)}.
		

Crossrefs

Cf. A384479, A386847.

Extensions

a(16)-a(18) from Sean A. Irvine, Aug 14 2025

More terms from Jinyuan Wang, Aug 29 2025