A362312 Sierpinski triangle read by rows and filled in the greedy way such that each row, each diagonal and each antidiagonal contains distinct nonnegative values.

0, 1, 2, 2, 1, 3, 0, 2, 4, 4, 3, 5, 1, 0, 6, 6, 0, 1, 5, 7, 3, 4, 2, 5, 8, 6, 9, 8, 7, 9, 4, 3, 8, 10, 3, 4, 11, 11, 5, 6, 0, 1, 3, 4, 10, 12, 2, 5, 13, 13, 6, 4, 1, 0, 7, 5, 12, 14, 5, 6, 7, 2, 3, 9, 15, 15, 7, 8, 1, 9, 0, 2, 5, 6, 4, 10, 11, 12, 13, 14, 16, 16, 14

Offset

0,3

Comments

This sequence is a variant of A296339.

The n-th row has A001316(n) terms, the first one being n and the last one being A361740(n).

Links

Rémy Sigrist, Table of n, a(n) for n = 0..6560 (rows for n = 0..255 flattened)

Rémy Sigrist, Colored representation of the first 512 rows (the hue is function of the terms, black pixels denote 0's, white pixels denote empty places)

Rémy Sigrist, C++ program

Example

Sierpinski triangle begins (with dots denoting empty places):
                                  0
                                1   2
                              2   .   1
                            3   0   2   4
                          4   .   .   .   3
                        5   1   .   .   0   6
                      6   .   0   .   1   .   5
                    7   3   4   2   5   8   6   9
                  8   .   .   .   .   .   .   .   7
                9   4   .   .   .   .   .   .   3   8
             10   .   3   .   .   .   .   .   4   .  11
           11   5   6   0   .   .   .   .   1   3   4  10
         12   .   .   .   2   .   .   .   5   .   .   .  13
       13   6   .   .   4   1   .   .   0   7   .   .   5  12
     14   .   5   .   6   .   7   .   2   .   3   .   9   .  15
   15   7   8   1   9   0   2   5   6   4  10  11  12  13  14  16

Prog

(C++) See Links section.

Crossrefs

Cf. A001316, A296339, A361740 (right border), A362313 (least values).

Sequence in context: A364493 A117046 A268192 * A333707 A077653 A077889

Adjacent sequences: A362309 A362310 A362311 * A362313 A362314 A362315

Keyword

nonn,tabf

Author

Rémy Sigrist, Apr 15 2023

Status

approved