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 A197819 #39 Nov 02 2022 07:41:43 %S A197819 0,1,0,3,2,1,0,15,10,5,12,3,6,9,8,7,2,13,4,11,14,1,0,255,170,85,204, %T A197819 51,102,153,136,119,34,221,68,187,238,17,240,15,90,165,60,195,150,105, %U A197819 120,135,210,45,180,75,30,225,160,95,10,245,108,147 %N A197819 Table of binary Walsh functions w(A001317), columns read as binary numbers. %C A197819 The rows of an infinite binary Walsh matrix (compare A228539) are the binary Walsh functions w(0),w(1),w(2),w(3),... %C A197819 This number triangle represents the infinite binary array w(1),w(3),w(5),w(15),... (1,3,5,15,... is A001317.) %C A197819 T(n,k) is column k of the (2^n) X (2^2^n) submatrix read as a binary number. %C A197819 Top left 4 X 16 submatrix of the binary array: %C A197819 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 %C A197819 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 %C A197819 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 %C A197819 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 %C A197819 In the sequence this is represented by row 2: %C A197819 0 15 10 5 12 3 6 9 8 7 2 13 4 11 14 1 %C A197819 A195467 is the infinite array of Gray code permutation powers. It can be defined by this binary array, which happens to be A195467 mod 2. %C A197819 Each odd column is the complement of the even column on its left. %C A197819 Each row of the number triangle is a self-inverse Walsh permutation. The subsequence of even entries (on the even places) divided by 2 is a self-inverse Walsh permutation too. %H A197819 Tilman Piesk, <a href="/A197819/b197819.txt">Rows 0..3 of the triangle, flattened</a> %H A197819 Tilman Piesk, permutation matrices of <a href="http://commons.wikimedia.org/wiki/File:Walsh_permutation_1_3_5_15.svg">row 2</a> and <a href="http://commons.wikimedia.org/wiki/File:Walsh_permutation_1_3_5_15_17_51_85_255.svg">row 3</a> %H A197819 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 A195467 %Y A197819 Cf. A195467 (consecutive powers of the Gray code permutation). %Y A197819 Cf. A001317 (Sierpinski triangle rows read like binary numbers). %K A197819 nonn,tabf %O A197819 0,4 %A A197819 _Tilman Piesk_, Oct 18 2011, reviewed Aug 25 2013