A386846 a(n) is the number of sets of distinct four-cuboid combinations that fill an n X n X n cube excluding combinations that contain strict cuboids.

0, 0, 2, 3, 4, 6, 6, 9, 8, 13, 11, 17, 15, 23, 20, 30, 27, 39, 36, 50, 47, 64, 61, 80, 78, 100, 98, 123, 122, 150, 150, 181, 182, 217, 219, 257, 261, 303, 308, 354, 361, 411, 420, 474, 485, 544, 557, 620, 636, 704, 722, 795, 816, 894, 918, 1001, 1028, 1117

Offset

1,3

Comments

A strict cuboid is a cuboid with all three dimensions different to each other.

Alternatively a(n) is number of ways to decompose (n,n,n) triplet into sets of distinct unordered geometrically feasible four triplets of the form (x,y,z) excluding x != y != z in any of the triplets.

Links

Table of n, a(n) for n=1..58.

Example

(5,5,5) triplet can be decomposed into sets of four triplets in 47 different ways and only the following 4 sets do not contain strict cuboids:
  {(5,5,1), (5,4,4), (4,1,1), (1,4,4)},
  {(5,5,3), (5,2,2), (3,3,2), (2,2,3)},
  {(5,5,2), (3,3,5), (2,2,3), (3,3,2)},
  {(4,1,1), (5,1,1), (1,4,4), (4,5,5)}.

Crossrefs

Column 4 of A386848.

Cf. A384311.

Sequence in context: A195013 A079667 A073061 * A390246 A300526 A006874

Adjacent sequences: A386843 A386844 A386845 * A386847 A386848 A386849

Keyword

nonn

Author

Janaka Rodrigo, Aug 05 2025

Extensions

More terms from Sean A. Irvine, Aug 06 2025

Status

approved