A386757 a(n) is the number of sets of noncongruent five-cuboid combinations that fill an n X n X n cube excluding combinations that contain cube-shaped cuboids.

0, 0, 1, 21, 179, 513, 1471, 2736, 5713, 8881, 15478, 21961, 34355, 45696, 66768, 84922, 117621, 145313, 193283, 232787, 300764, 355093, 447181, 520412, 641801, 736900, 894222, 1015173, 1213646, 1366103, 1612366, 1799756, 2102572, 2329955, 2695421, 2970037, 3406356

Offset

1,4

Comments

Alternatively a(n) is the number of ways to decompose (n,n,n) triplet into sets of distinct five unordered triplets of the form (x,y,z) without having x = y = z in any of the triplets.

Links

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

Example

There are 31 sets of distinct unordered five-cuboid combinations filling 4 X 4 X 4 cube including 10 combinations containing cube-shaped cuboids which are listed below,
   {(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)},
   {(1,1,1), (1,1,3), (1,1,4), (1,2,4), (3,4,4)},
   {(1,1,1), (1,1,3), (1,1,4), (2,3,4), (2,4,4)},
   {(1,1,1), (1,1,3), (1,2,4), (1,4,4), (3,3,4)},
   {(1,1,1), (1,1,3), (1,3,4), (1,4,4), (2,4,4)},
   {(1,1,3), (1,2,3), (1,3,4), (1,4,4), (3,3,3)},
   {(1,1,4), (1,2,4), (1,3,3), (1,4,4), (3,3,3)},
   {(1,2,2), (1,2,4), (2,2,2), (2,2,3), (2,4,4)},
   {(1,2,2), (1,4,4), (2,2,2), (2,2,3), (2,3,4)}.
Therefore a(4) = 31 - 10 = 21.

Crossrefs

Column 5 of A386779.

Cf. A384479.

Sequence in context: A090021 A254681 A219625 * A244875 A025604 A219412

Adjacent sequences: A386754 A386755 A386756 * A386758 A386759 A386760

Keyword

nonn

Author

Janaka Rodrigo, Aug 01 2025

Extensions

a(14)-a(16) from Sean A. Irvine, Aug 03 2025

a(17)-a(37) from Jinyuan Wang, Aug 04 2025

Status

approved