A384479 -id:A384479 - cp's OEIS frontend

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

Janaka Rodrigo, Aug 07 2025

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.

			(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)}.

Cf. A384479, A386847.

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

More terms from Jinyuan Wang, Aug 29 2025

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.

Original entry on oeis.org

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

Janaka Rodrigo, Aug 14 2025

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.

			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.

Cf. A384479, A385580, A387121.

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

More terms from Jinyuan Wang, Aug 29 2025

cp's OEIS Frontend

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

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