A387040 a(n) is the number of distinct five-cuboid combinations that fill an n X n X n cube with cuboids of different volumes.

0, 0, 2, 26, 206, 442, 1531, 2661, 5574, 8514, 15614, 20331, 34500, 44814, 64503, 83143, 117759, 141290, 193436, 226722, 295978, 351953, 447208, 507508, 637447, 732322, 887044, 1001577, 1213233, 1337525, 1611692, 1786560, 2088648, 2321052, 2673275, 2929254, 3404667

Offset

1,3

Comments

Alternatively a(n) is the number of ways to decompose (n,n,n) triplet into geometrically feasible five distinct unordered triplets of the form (x,y,z) with no pair having equal value for the product x*y*z.

Links

Table of n, a(n) for n=1..37.

Example

According to A384479(5), (5,5,5) triplet can be decomposed into 209 distinct sets of five triplets and only three of them contain pair of triplets with equal value for x*y*z. Those are,
   {(1,2,5), (1,3,5), (1,4,5), (2,2,5), (3,4,5)},
   {(1,1,5), (1,4,5), (2,2,5), (2,3,5), (2,5,5)},
   {(1,3,5), (1,4,5), (2,2,5), (2,3,5), (2,4,5)}.
Therefore a(5) = 209-3 = 206.

Crossrefs

Column 5 of A387121.

Cf. A384479, A385580.

Sequence in context: A072415 A197468 A184354 * A178884 A211319 A121768

Adjacent sequences: A387037 A387038 A387039 * A387041 A387042 A387043

Keyword

nonn

Author

Janaka Rodrigo, Aug 14 2025

Extensions

a(15)-a(16) from Sean A. Irvine, Aug 19 2025

More terms from Jinyuan Wang, Aug 29 2025

Status

approved