cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

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%I A319900 #30 Sep 21 2019 14:42:30
%S A319900 1,24,14515200,7708721243457872461824000
%N 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.
%C A319900 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 A319900 Bert Dobbelaere, <a href="/A319900/a319900.cpp.txt">C++ program for a(4)</a>
%H A319900 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 A319900 The Art of Puzzles, <a href="https://www.gmpuzzles.com/blog/2013/02/dr-sudoku-prescribes-38-sudo-kurve/">Sudo-Kurve 38</a>
%F A319900 Observation: a(n) = A010791(n*(n-1)) for 1 <= n <= 3. - _Omar E. Pol_, Oct 02 2018
%e A319900 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 A319900 Cf. A107739, A109741.
%K A319900 bref,nonn,more
%O A319900 1,2
%A A319900 _Tanya Khovanova_ and _Wayne Zhao_, Sep 30 2018
%E A319900 a(4) from _Bert Dobbelaere_, Sep 20 2019