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

1,2

Comments

When n = 3, this is equivalent to enumerating the different fill-ins of a Sudo-Kurve puzzle of the shape given in the link 'Sudo-Kurve 38'.

Links

Table of n, a(n) for n=1..4.

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

Example

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.

Crossrefs

Cf. A107739, A109741.

Sequence in context: A013820 A294326 A255322 * A172803 A141643 A275026

Adjacent sequences: A319897 A319898 A319899 * A319901 A319902 A319903

Keyword

bref,nonn,more

Author

Tanya Khovanova and Wayne Zhao, Sep 30 2018

Extensions

a(4) from Bert Dobbelaere, Sep 20 2019

Status

approved