A384743 a(n) is the number of distinct five-cuboid combinations filling n X n X n cube without allowing a cut spanning through the full cube in any of filling positions.

0, 0, 0, 1, 6, 20, 50, 110, 197, 343, 535, 814, 1171, 1651, 2240, 2996, 3900, 5019, 6333, 7918, 9744, 11905, 14366, 17225, 20451, 24146, 28274, 32955, 38143, 43967, 50380, 57520, 65335, 73976, 83386, 93720, 104925, 117165, 130377, 144743, 160190, 176909, 194831

Offset: 1

Author

Janaka Rodrigo, Jun 08 2025

Keywords

• nonn

Comments

Alternatively a(n) is the number of distinct five-triplet sets of the terms produced by D(n)-A(n); that is, a(n) = |D(n)-A(n)|, where 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)}}.
D(3)-A(3) = {}.
Therefore, a(3) = 0.
		

Links

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

Crossrefs

Cf. A381847, A384208, A384311, A384479, A384737.

Extensions

a(11)-a(43) from Jinyuan Wang, Aug 04 2025