A384737 a(n) is the number of distinct five-cuboid combinations filling an n X n X n cube only with at least one cut spanning through the full cube.

0, 0, 1, 27, 195, 527, 1487, 2711, 5648, 8694, 15163, 21398, 33514, 44411, 64990, 82431, 114337, 140958, 187742, 225716, 292010, 344238, 434025, 504464, 622802, 714278, 867664, 984013, 1177505, 1324222, 1564296, 1744637, 2039877, 2258715, 2615027, 2879412, 3304797

Offset: 1

Author

Janaka Rodrigo, Jun 08 2025

Keywords

• nonn

Comments

Alternatively a(n) is the number of distinct five-triplet sets produced by A(n)-D(n); that is, a(n) = |A(n)-D(n)|, where the sequences of sets A(n), B(n) and C(n) are introduced in A384479 and D(n) = B(n) U C(n).

Examples

			A(3) = {{(1,1,2), (1,1,3), (1,2,2), (1,2,3), (2,2,3)}, {(1,1,1), (1,1,2), (1,1,3), (1,3,3), (2,2,3)}}.
B(3) = {{(1,1,2), (1,1,3), (1,2,2), (1,2,3), (2,2,3)}}.
C(3) = {}.
D(3) = B(3) U C(3) = {{(1,1,2), (1,1,3), (1,2,2), (1,2,3), (2,2,3)}}.
A(3)-D(3) = {{(1,1,1), (1,1,2), (1,1,3), (1,3,3), (2,2,3)}}.
Therefore, a(3) = 1.
		

Links

• Janaka Rodrigo, Sets of A(n)-D(n) in Triplets Form

Crossrefs

Cf. A381847, A384208, A384311, A384479, A384743.

Extensions

a(11)-a(37) from Jinyuan Wang, Aug 04 2025