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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
1, 24, 14515200, 7708721243457872461824000 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A013820 A294326 A255322 * A172803 A141643 A275026
KEYWORD
bref,nonn,more
AUTHOR
Tanya Khovanova and Wayne Zhao, Sep 30 2018
EXTENSIONS
a(4) from Bert Dobbelaere, Sep 20 2019
STATUS
approved

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Last modified April 22 02:54 EDT 2024. Contains 371887 sequences. (Running on oeis4.)