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

0,3

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.

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

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).

Example

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

Prog

(PARI) See Links section.

Crossrefs

Cf. A326757, A326758, A326759.

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

Sequence in context: A360104 A356670 A071494 * A071495 A071515 A121998

Adjacent sequences: A326761 A326762 A326763 * A326765 A326766 A326767

Keyword

nonn,tabf

Author

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

Status

approved