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A104894 Binary array, related to the Thue-Morse sequence A010060, read by downward antidiagonals.

%I A104894 #19 Apr 04 2024 10:04:59
%S A104894 0,1,0,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,1,
%T A104894 1,0,0,0,0,0,1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,0,1,1,
%U A104894 1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0,1,1
%N A104894 Binary array, related to the Thue-Morse sequence A010060, read by downward antidiagonals.
%H A104894 Paolo Xausa, <a href="/A104894/b104894.txt">Table of n, a(n) for n = 0..11324</a> (first 150 antidiagonals, flattened).
%H A104894 David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [<a href="http://neilsloane.com/doc/slopey.pdf">pdf</a>, <a href="http://neilsloane.com/doc/slopey.ps">ps</a>].
%F A104894 T(n,k) = A010060(k mod 2^(n+1)). - _Paolo Xausa_, Apr 04 2024
%e A104894 Row n consists of repetitions of the first 2^(n+1) terms of A010060:
%e A104894 .
%e A104894  n\k| 0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15  ...
%e A104894 ---------------------------------------------------------
%e A104894   0 | 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, ...
%e A104894   1 | 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, ...
%e A104894   2 | 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, ...
%e A104894   3 | 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, ...
%e A104894   4 | 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, ...
%e A104894   5 | 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, ...
%e A104894   6 | 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, ...
%e A104894   7 | 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, ...
%e A104894   ...
%e A104894 Columns written in base 10 (see Table 2 of reference) give 0, -1, -2, 1, -4, 3, 2, -3, -8, 7, 6, -7, 4, -5, -6, 5, ... (see A104895).
%t A104894 Table[ThueMorse[Mod[n-k, 2^(k+1)]], {n, 0, 15}, {k, 0, n}] (* _Paolo Xausa_, Apr 04 2024 *)
%Y A104894 Cf. A010060, A104895.
%K A104894 nonn,tabl
%O A104894 0,1
%A A104894 _Philippe Deléham_, Apr 24 2005
%E A104894 a(48) = 0 removed by _Paolo Xausa_, Apr 04 2024