A319900 a(n) is the number of distinct ways to arrange n copies of each of the numbers 1 through n^2 inside a fixed n X n X n cube, provided that no number appears twice in the same left-right plane, front-back plane, or top-bottom plane.
1, 24, 14515200, 7708721243457872461824000
Offset: 1
Examples
For n = 2, the top layer of the 2 X 2 X 2 cube must contain each of the numbers 1, 2, 3, 4. This can be arranged in 24 ways. Each way uniquely determines the rest of the cube, so there are 24 possible cubes.
Links
- Bert Dobbelaere, C++ program for a(4)
- T. Khovanova and W. Zhao, Mathematics of a Sudo-Kurve, arXiv:1808.06713 [math.HO], 2018.
- The Art of Puzzles, Sudo-Kurve 38
Formula
Observation: a(n) = A010791(n*(n-1)) for 1 <= n <= 3. - Omar E. Pol, Oct 02 2018
Extensions
a(4) from Bert Dobbelaere, Sep 20 2019
Comments