This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A195467 #84 Dec 16 2017 23:29:41 %S A195467 0,1,0,1,2,3,0,1,3,2,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,0,1,3,2,6, %T A195467 7,5,4,12,13,15,14,10,11,9,8,0,1,2,3,5,4,7,6,10,11,8,9,15,14,13,12,0, %U A195467 1,3,2,7,6,4,5,15,14,12,13,8,9,11,10 %N A195467 Consecutive powers of the Gray code permutation. %C A195467 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. %C A195467 The different powers of the n-bit GCP form a matrix of size (A062383(n-1)) X (2^n). %C A195467 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: %C A195467 The 1-bit GCP is the identity permutation: %C A195467 0: 0 1 %C A195467 The 2 different powers of the 2-bit GCP: %C A195467 0: 0 1 2 3 %C A195467 1: 0 1 3 2 %C A195467 The 4 different powers of the 4-bit GCP: %C A195467 0: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 %C A195467 1: 0 1 3 2 6 7 5 4 12 13 15 14 10 11 9 8 %C A195467 2: 0 1 2 3 5 4 7 6 10 11 8 9 15 14 13 12 %C A195467 3: 0 1 3 2 7 6 4 5 15 14 12 13 8 9 11 10 %C A195467 . %C A195467 This array A can be defined using the binary array B = A197819 by %C A195467 A = B + 2 * 2stretched(B) + 4 * 4stretched(B) + 8 * 8stretched(B) + ... %C A195467 where nstretched has the following meaning: %C A195467 2stretched(1,2,3,4,...) = 1,1,2,2,3,3,4,4,... %C A195467 4stretched(1,2,3,4,...) = 1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,... %C A195467 etc. %H A195467 Tilman Piesk, <a href="/A195467/b195467.txt">First 15 rows of the triangle, flattened</a> %H A195467 Tilman Piesk, <a href="/A195467/a195467_7.txt">Explanations</a> (including the 8x256 submatrix) and <a href="/A195467/a195467_5.txt">MATLAB code</a> showing the connection with A197819 %H A195467 Tilman Piesk, <a href="/A195467/a195467_1.txt">The 8 different powers of the 6-bit Gray code permutation</a> %H A195467 Tilman Piesk, <a href="http://en.wikiversity.org/wiki/Gray_code_permutation_powers">Gray code permutation powers</a> (Wikiversity) %Y A195467 Cf. A003188 (Gray code permutation). %Y A195467 Cf. A006068 (inverse of the Gray code permutation). %Y A195467 Cf. A064706 (square of the Gray code permutation). %Y A195467 Cf. A197819 (this array mod 2). %K A195467 nonn,tabf %O A195467 0,5 %A A195467 _Tilman Piesk_, Sep 23 2011 %E A195467 Huge edit by _Tilman Piesk_, Aug 25 2013