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

Author

Janaka Rodrigo, Aug 01 2025

Keywords

• nonn

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.

Examples

			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

Cf. A384479, A386779.

Extensions

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

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