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

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, 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, 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

Offset

0,1

Links

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

David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [pdf, ps].

Formula

T(n,k) = A010060(k mod 2^(n+1)). - Paolo Xausa, Apr 04 2024

Example

Row n consists of repetitions of the first 2^(n+1) terms of A010060:
.
 n\k| 0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15  ...
---------------------------------------------------------
  0 | 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, ...
  1 | 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, ...
  2 | 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, ...
  3 | 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, ...
  4 | 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, ...
  5 | 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, ...
  6 | 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, ...
  7 | 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, ...
  ...
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).

Mathematica

Table[ThueMorse[Mod[n-k, 2^(k+1)]], {n, 0, 15}, {k, 0, n}] (* Paolo Xausa, Apr 04 2024 *)

Crossrefs

Cf. A010060, A104895.

Sequence in context: A285411 A372544 A104893 * A168393 A071986 A079944

Adjacent sequences: A104891 A104892 A104893 * A104895 A104896 A104897

Keyword

nonn,tabl

Author

Philippe Deléham, Apr 24 2005

Extensions

a(48) = 0 removed by Paolo Xausa, Apr 04 2024

Status

approved