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A161175
Triangle read by rows, modified Thue-Morse sequence (A010060 with offset 1): change 0 to 2, else 1.
3
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
KEYWORD
nonn,tabf
AUTHOR
Gary W. Adamson, Jun 05 2009
STATUS
approved