A161175 Triangle read by rows, modified Thue-Morse sequence (A010060 with offset 1): change 0 to 2, else 1.

1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2

Offset

1,3

Comments

Row sums = A003945: (1, 3, 6, 12, 24,...).

Rows tend to A001285: (1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2,...).

Links

Paolo Xausa, Table of n, a(n) for n = 1..8191 (rows 1..13 of the triangle, flattened).

Formula

Given A010060 starting with offset 1, change zeros to 2, retain 1's.

By rows, (n+1)-th row = n-th row with n-th row appended under morphism 1->2, 2->1.

Example

First few rows of the triangle =
  1;
  1, 2;
  1, 2, 2, 1;
  1, 2, 2, 1, 2, 1, 1, 2;
  1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1;
  ...
Given A010060 starting with 1 (below, top row); 0->2, else 1:
  A010060: (1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1,...)
  A161175: (1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1,...)
Triangle read by rows, row 4 = (1, 2, 2, 1, 2, 1, 1, 2) = (2, 1, 1, 2) appended to the right of (1, 2, 2, 1).

Mathematica

ReplaceAll[ThueMorse[Range[127]], 0->2] (* Paolo Xausa, Dec 18 2023 *)

Crossrefs

Cf. A010060, A001285, A003945

Sequence in context: A372469 A265918 A207676 * A356515 A095955 A272772

Adjacent sequences: A161172 A161173 A161174 * A161176 A161177 A161178

Keyword

nonn,tabf

Author

Gary W. Adamson, Jun 05 2009

Status

approved