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

Author

Gary W. Adamson, Jun 05 2009

Keywords

• nonn
• tabf

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,...).

Examples

			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).
		

Links

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

Crossrefs

Cf. A010060, A001285, A003945

Programs

Mathematica

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

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.