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
Keywords
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.
Extensions
a(14)-a(16) from Sean A. Irvine, Aug 03 2025
a(17)-a(37) from Jinyuan Wang, Aug 04 2025
Comments