login
A386884
a(n) is the number of distinct four-cuboid combinations that fill an n X n X n cube using only strict cuboids.
1
0, 0, 0, 0, 1, 2, 9, 12, 30, 36, 70, 80, 135, 150, 231, 252, 364, 392, 540, 576, 765, 810, 1045, 1100, 1386, 1452, 1794, 1872, 2275, 2366, 2835, 2940, 3480, 3600, 4216, 4352, 5049, 5202, 5985, 6156, 7030, 7220, 8190, 8400, 9471, 9702, 10879, 11132, 12420
OFFSET
1,6
COMMENTS
A strict cuboid is a cuboid with all three dimensions different.
Alternatively a(n) is the number of ways to decompose triplet (n,n,n) into sets of distinct four unordered triplets of the form (x,y,z) with x != y != z for each of the four triplets.
EXAMPLE
As described in A384311 there are 85 sets of distinct four-cuboid combinations filling 6 X 6 X 6 cube and only two of those have all four triplets with different elements, those are;
{(1,2,6), (1,4,6), (2,5,6), (4,5,6)},
{(1,3,6), (2,3,6), (3,4,6), (3,5,6)}.
Therefore a(6) = 2.
CROSSREFS
Column 4 of A386903.
Cf. A384311.
Sequence in context: A337360 A340038 A178312 * A347495 A253608 A126977
KEYWORD
nonn
AUTHOR
Janaka Rodrigo, Aug 06 2025
EXTENSIONS
More terms from Sean A. Irvine, Aug 06 2025
STATUS
approved