A221146 Table read by antidiagonals: (m+n) - (m XOR n).

0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 0, 0, 4, 4, 0, 0, 0, 2, 0, 6, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 2, 8, 2, 4, 2, 0, 0, 0, 4, 4, 8, 8, 4, 4, 0, 0, 0, 2, 0, 6, 8, 10, 8, 6, 0, 2, 0, 0, 0, 0, 0, 8, 8, 8, 8, 0, 0, 0, 0, 0, 2, 4, 2, 0, 10, 12, 10, 0, 2, 4, 2, 0

Offset: 0

Author

BOCUT Adrian Sebastian, Dec 12 2012

Keywords

• nonn
• tabl
• look

Comments

Equals twice A004198.

This sequence is related to two fractals: the Sierpinski gasket fractal and Peano filigree.

For the Sierpinski fractal the procedure is the following:

- write the number stored in the position (i,j) as i+j + d, where d stands for difference.

The array of the differences is

0 0 0 0

0 2 0 2

0 0 4 4

0 2 4 6

If this matrix is represented by colors we obtain the Sierpinski gasket; coordinates (i,j) contain a pixel with the color i XOR j.

If we follow the odd and even numbers of the XOR table we obtain the Peano curve.

Examples

			Table begins:
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0 ...
0   2   0   2   0   2   0   2   0   2   0   2   0   2   0   2 ...
0   0   4   4   0   0   4   4   0   0   4   4   0   0   4   4 ...
0   2   4   6   0   2   4   6   0   2   4   6   0   2   4   6 ...
0   0   0   0   8   8   8   8   0   0   0   0   8   8   8   8 ...
0   2   0   2   8  10   8  10   0   2   0   2   8  10   8  10 ...
0   0   4   4   8   8  12  12   0   0   4   4   8   8  12  12 ...
0   2   4   6   8  10  12  14   0   2   4   6   8  10  12  14 ...
0   0   0   0   0   0   0   0  16  16  16  16  16  16  16  16 ...
0   2   0   2   0   2   0   2  16  18  16  18  16  18  16  18 ...
0   0   4   4   0   0   4   4  16  16  20  20  16  16  20  20 ...
0   2   4   6   0   2   4   6  16  18  20  22  16  18  20  22 ...
0   0   0   0   8   8   8   8  16  16  16  16  24  24  24  24 ...
0   2   0   2   8  10   8  10  16  18  16  18  24  26  24  26 ...
0   0   4   4   8   8  12  12  16  16  20  20  24  24  28  28 ...
0   2   4   6   8  10  12  14  16  18  20  22  24  26  28  30 ...
...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 0..11324 (first 150 antidiagonals, flattened).

Crossrefs

Cf. A003987, A004198.

Programs

Mathematica

Table[m-BitXor[n, m-n], {m, 0, 15}, {n, 0, m}] (* Paolo Xausa, Mar 14 2024 *)

Extensions

Edited by N. J. A. Sloane, Jan 03 2013