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

1,4

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).

Links

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

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

Example

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.

Crossrefs

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

Sequence in context: A365890 A365884 A042416 * A216108 A216110 A216112

Adjacent sequences: A384734 A384735 A384736 * A384738 A384739 A384740

Keyword

nonn

Author

Janaka Rodrigo, Jun 08 2025

Extensions

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

Status

approved