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%I #30 Mar 14 2024 04:51:26
%S 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,
%T 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,
%U 0,0,8,8,8,8,0,0,0,0,0,2,4,2,0,10,12,10,0,2,4,2,0
%N Table read by antidiagonals: (m+n) - (m XOR n).
%C Equals twice A004198.
%C This sequence is related to two fractals: the Sierpinski gasket fractal and Peano filigree.
%C For the Sierpinski fractal the procedure is the following:
%C - write the number stored in the position (i,j) as i+j + d, where d stands for difference.
%C The array of the differences is
%C 0 0 0 0
%C 0 2 0 2
%C 0 0 4 4
%C 0 2 4 6
%C If this matrix is represented by colors we obtain the Sierpinski gasket; coordinates (i,j) contain a pixel with the color i XOR j.
%C If we follow the odd and even numbers of the XOR table we obtain the Peano curve.
%H Paolo Xausa, <a href="/A221146/b221146.txt">Table of n, a(n) for n = 0..11324</a> (first 150 antidiagonals, flattened).
%e Table begins:
%e 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...
%e 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 ...
%e 0 0 4 4 0 0 4 4 0 0 4 4 0 0 4 4 ...
%e 0 2 4 6 0 2 4 6 0 2 4 6 0 2 4 6 ...
%e 0 0 0 0 8 8 8 8 0 0 0 0 8 8 8 8 ...
%e 0 2 0 2 8 10 8 10 0 2 0 2 8 10 8 10 ...
%e 0 0 4 4 8 8 12 12 0 0 4 4 8 8 12 12 ...
%e 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 ...
%e 0 0 0 0 0 0 0 0 16 16 16 16 16 16 16 16 ...
%e 0 2 0 2 0 2 0 2 16 18 16 18 16 18 16 18 ...
%e 0 0 4 4 0 0 4 4 16 16 20 20 16 16 20 20 ...
%e 0 2 4 6 0 2 4 6 16 18 20 22 16 18 20 22 ...
%e 0 0 0 0 8 8 8 8 16 16 16 16 24 24 24 24 ...
%e 0 2 0 2 8 10 8 10 16 18 16 18 24 26 24 26 ...
%e 0 0 4 4 8 8 12 12 16 16 20 20 24 24 28 28 ...
%e 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 ...
%e ...
%t Table[m-BitXor[n, m-n], {m, 0, 15}, {n, 0, m}] (* _Paolo Xausa_, Mar 14 2024 *)
%Y Cf. A003987, A004198.
%K nonn,tabl,look
%O 0,5
%A _BOCUT Adrian Sebastian_, Dec 12 2012
%E Edited by _N. J. A. Sloane_, Jan 03 2013
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