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

1,6

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.

Links

Table of n, a(n) for n=1..41.

Example

(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

Column 5 of A386903.

Cf. A384479, A386847.

Sequence in context: A305018 A041628 A022145 * A284659 A143666 A139757

Adjacent sequences: A386899 A386900 A386901 * A386903 A386904 A386905

Keyword

nonn

Author

Janaka Rodrigo, Aug 07 2025

Extensions

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

More terms from Jinyuan Wang, Aug 29 2025

Status

approved