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.

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, 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, 11, 4, 12, 14, 2, 0, 7, 8, 3, 6, 5, 2, 8, 2, 0, 1, 3, 4, 5

Offset: 0

Author

Rémy Sigrist and N. J. A. Sloane, Jul 24 2019

Keywords

• nonn
• tabf

Comments

The triangle is read by increasing x+y+z and then increasing x+y and then increasing x.

The sequences A326757, A326758 and A326759 give the X-, Y- and Z-coordinates, respectively, of the 0's in array T.

Examples

			Array T(x,y,z) begins:
- z=3:
      0| 3
    ---+--
    x/y| 0
- z=2:
      1| 0
      0| 2 6
    ---+----
    x/y| 0 1
- z=1:
      2| 5
      1| 4 7
      0| 1 5 0
    ---+------
    x/y| 0 1 2
- z=0:
      3| 4
      2| 1 0
      1| 2 6 1
      0| 0 3 4 2
    ---+--------
    x/y| 0 1 2 3
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10659 (T(x,y,z) such that x+y+z < 39)
• Rémy Sigrist, Colored representation of the sequence alongside the faces of the tetrahedron defined by x, y, z >= 0 and x+y+z < 500
• Rémy Sigrist, PARI program for A326764

Crossrefs

Cf. A326757, A326758, A326759.

Cf. A326765, A326766, A326767, A326768, A326769, A326770.

Programs

PARI

See Links section.

Formula

T(A326757(n), A326758(n), A326759(n)) = 0.

T(x, 0, 0) = A326765(x).

T(0, y, 0) = A326766(y).

T(0, 0, z) = z.

T(x, x, x) = A326767(x).

T(0, y, y) = A326768(y).

T(x, 0, x) = A326769(x).

T(x, x, 0) = A326770(x).