OFFSET
0,5
COMMENTS
The powers of the Gray code permutation (GCP, A003188) form an infinite array, where row n is the n-th power of the GCP. Row 0 is the identity permutation (i.e., the sequence of nonnegative integers), and row 1 is the GCP itself.
The different powers of the n-bit GCP form a matrix of size (A062383(n-1)) X (2^n).
This sequence represents the infinite array in a somewhat redundant way: It shows the rows of all the (2^n) X (2^2^n) matrices of powers of (2^n)-bit GCP. So this sequence forms a triangle, and these 3 matrices are its first 7 rows:
The 1-bit GCP is the identity permutation:
0: 0 1
The 2 different powers of the 2-bit GCP:
0: 0 1 2 3
1: 0 1 3 2
The 4 different powers of the 4-bit GCP:
0: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1: 0 1 3 2 6 7 5 4 12 13 15 14 10 11 9 8
2: 0 1 2 3 5 4 7 6 10 11 8 9 15 14 13 12
3: 0 1 3 2 7 6 4 5 15 14 12 13 8 9 11 10
.
This array A can be defined using the binary array B = A197819 by
A = B + 2 * 2stretched(B) + 4 * 4stretched(B) + 8 * 8stretched(B) + ...
where nstretched has the following meaning:
2stretched(1,2,3,4,...) = 1,1,2,2,3,3,4,4,...
4stretched(1,2,3,4,...) = 1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,...
etc.
LINKS
Tilman Piesk, First 15 rows of the triangle, flattened
Tilman Piesk, Explanations (including the 8x256 submatrix) and MATLAB code showing the connection with A197819
Tilman Piesk, Gray code permutation powers (Wikiversity)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Tilman Piesk, Sep 23 2011
EXTENSIONS
Huge edit by Tilman Piesk, Aug 25 2013
STATUS
approved