|
%I #30 Sep 21 2019 14:42:30
%S 1,24,14515200,7708721243457872461824000
%N 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.
%C 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'.
%H Bert Dobbelaere, <a href="/A319900/a319900.cpp.txt">C++ program for a(4)</a>
%H T. Khovanova and W. Zhao, <a href="http://arxiv.org/abs/1808.06713">Mathematics of a Sudo-Kurve</a>, arXiv:1808.06713 [math.HO], 2018.
%H The Art of Puzzles, <a href="https://www.gmpuzzles.com/blog/2013/02/dr-sudoku-prescribes-38-sudo-kurve/">Sudo-Kurve 38</a>
%F Observation: a(n) = A010791(n*(n-1)) for 1 <= n <= 3. - _Omar E. Pol_, Oct 02 2018
%e 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.
%Y Cf. A107739, A109741.
%K bref,nonn,more
%O 1,2
%A _Tanya Khovanova_ and _Wayne Zhao_, Sep 30 2018
%E a(4) from _Bert Dobbelaere_, Sep 20 2019
| 