A386847 a(n) is the number of sets of distinct five-cuboid combinations that fill an n X n X n cube excluding combinations that contain strict cuboids.

0, 0, 1, 3, 10, 19, 30, 44, 64, 84, 100, 141, 150, 202, 218, 279, 282, 382, 365, 478, 470, 603, 568, 749, 690, 897, 840, 1066, 980, 1279, 1151, 1473, 1357, 1716, 1552, 1988, 1785, 2265, 2062, 2573, 2327, 2947, 2640, 3296, 3006, 3718, 3361, 4182, 3774, 4659, 4251

Offset

1,4

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 five 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..51.

Example

(4,4,4) triplet can be decomposed into sets of five triplets in 31 different ways and only the following three sets do not contain strict cuboids:
  {(1,1,1), (1,1,2), (1,1,4), (1,3,3), (3,4,4)},
  {(1,1,1), (1,1,2), (1,3,3), (1,4,4), (3,3,4)},
  {(1,1,3), (1,1,4), (1,3,3), (1,4,4), (2,4,4)}.

Crossrefs

Column 5 of A386848.

Cf. A384479.

Sequence in context: A321543 A212456 A028878 * A010896 A234940 A135446

Adjacent sequences: A386844 A386845 A386846 * A386848 A386849 A386850

Keyword

nonn

Author

Janaka Rodrigo, Aug 05 2025

Extensions

a(16)-a(39) from Sean A. Irvine, Aug 06 2025

More terms from Jinyuan Wang, Aug 10 2025

Status

approved