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
Examples
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.
Extensions
a(15)-a(16) from Sean A. Irvine, Aug 19 2025
More terms from Jinyuan Wang, Aug 29 2025
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