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A326764 Lexicographically earliest array T(x,y,z) of nonnegative integers with x, y, z >= 0, such that the terms alongside any line parallel to any of the 13 axes of rotation of a cube are distinct.

%I A326764 #21 Feb 03 2023 02:44:48
%S A326764 0,1,2,3,2,4,5,1,6,4,3,0,6,5,7,0,4,0,1,2,4,1,7,3,8,9,2,9,10,3,5,10,8,
%T A326764 7,1,5,6,0,2,5,10,7,11,12,1,0,6,4,11,8,3,1,5,9,0,6,6,3,1,0,9,8,5,4,13,
%U A326764 11,4,12,14,2,0,7,8,3,6,5,2,8,2,0,1,3,4,5
%N A326764 Lexicographically earliest array T(x,y,z) of nonnegative integers with x, y, z >= 0, such that the terms alongside any line parallel to any of the 13 axes of rotation of a cube are distinct.
%C A326764 The triangle is read by increasing x+y+z and then increasing x+y and then increasing x.
%C A326764 The sequences A326757, A326758 and A326759 give the X-, Y- and Z-coordinates, respectively, of the 0's in array T.
%H A326764 Rémy Sigrist, <a href="/A326764/b326764.txt">Table of n, a(n) for n = 0..10659</a> (T(x,y,z) such that x+y+z < 39)
%H A326764 Rémy Sigrist, <a href="/A326764/a326764.png">Colored representation of the sequence alongside the faces of the tetrahedron defined by x, y, z >= 0 and x+y+z < 500</a>
%H A326764 Rémy Sigrist, <a href="/A326764/a326764.gp.txt">PARI program for A326764</a>
%F A326764 T(A326757(n), A326758(n), A326759(n)) = 0.
%F A326764 T(x, 0, 0) = A326765(x).
%F A326764 T(0, y, 0) = A326766(y).
%F A326764 T(0, 0, z) = z.
%F A326764 T(x, x, x) = A326767(x).
%F A326764 T(0, y, y) = A326768(y).
%F A326764 T(x, 0, x) = A326769(x).
%F A326764 T(x, x, 0) = A326770(x).
%e A326764 Array T(x,y,z) begins:
%e A326764 - z=3:
%e A326764       0| 3
%e A326764     ---+--
%e A326764     x/y| 0
%e A326764 - z=2:
%e A326764       1| 0
%e A326764       0| 2 6
%e A326764     ---+----
%e A326764     x/y| 0 1
%e A326764 - z=1:
%e A326764       2| 5
%e A326764       1| 4 7
%e A326764       0| 1 5 0
%e A326764     ---+------
%e A326764     x/y| 0 1 2
%e A326764 - z=0:
%e A326764       3| 4
%e A326764       2| 1 0
%e A326764       1| 2 6 1
%e A326764       0| 0 3 4 2
%e A326764     ---+--------
%e A326764     x/y| 0 1 2 3
%o A326764 (PARI) See Links section.
%Y A326764 Cf. A326757, A326758, A326759.
%Y A326764 Cf. A326765, A326766, A326767, A326768, A326769, A326770.
%K A326764 nonn,tabf
%O A326764 0,3
%A A326764 _Rémy Sigrist_ and _N. J. A. Sloane_, Jul 24 2019