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 A239304 #50 Dec 17 2017 03:17:20 %S A239304 1,1,2,3,1,2,4,2,1,3,2,5,4,1,3,2,5,6,3,1,4,6,2,3,7,5,1,4,7,3,2,6,8,4, %T A239304 1,5,3,8,7,2,4,9,6,1,5,3,8,9,4,2,7,10,5,1,6,9,3,4,10,8,2,5,11,7,1,6, %U A239304 10,4,3,9 %N A239304 Triangle of permutations corresponding to the compressed square roots of Gray code * bit-reversal permutation (A239303). %C A239304 The symmetrical binary matrices corresponding to the rows of A239303 can be interpreted as adjacency matrices of undirected graphs. These graphs are chains where one end is connected to itself, so they can be interpreted as permutations. The end connected to itself is always the first element of the permutation, i.e., on the left side of the triangle. %C A239304 Columns of the square array: %C A239304 T(m,1) = A008619(m) = 1,2,2,3,3... %C A239304 T(m,2) = 1,1,1... %C A239304 T(m,3) = A028242(m+3) = 3,2,4,3,5,4,6,5,7,6,8,7,9,8,10,9,11,10,12... %C A239304 T(m,4) = m+3 = 4,5,6... %C A239304 T(m,5) = A084964(m+4) = 2,5,3,6,4,7,5,8,6,9,7,10,8,11,9,12,10,13... %C A239304 T(m,6) = 2,2,2... %C A239304 T(m,7) = A168230(m+5) = 6,3,7,4,8,5,9,6,10,7,11,8,12,9,13,10,14... %C A239304 T(m,8) = m+6 = 7,8,9... %C A239304 T(m,9) = A152832(m+9) = 3,8,4,9,5,10,6,11,7,12,8,13,9,14,10,15... %C A239304 T(m,10) = 3,3,3... %C A239304 Diagonals of the square array: %C A239304 T(n,n) = a(A001844(n)) = 1,1,4,7,4,2,9,14,7,3,14,21,10,4,19,28,13,5,24... %C A239304 T(n,2n-1) = a(A064225(n)) = 1,2,3... %C A239304 T(2n-1,n) = a(A081267(n)) = 1,1,5,10,6,2,12,21,11,3,19,32,16,4,26,43,21... %H A239304 Tilman Piesk, <a href="/A239304/b239304.txt">First 140 rows of the triangle, flattened</a> %H A239304 Tilman Piesk, <a href="https://en.wikiversity.org/wiki/Walsh_permutation;_sequency_ordered_Walsh_matrix">Sequency ordered Walsh matrix</a> (Wikiversity) %H A239304 Tilman Piesk, <a href="http://pastebin.com/XDhZLaGy">Calculation in MATLAB</a> %e A239304 Triangular array begins: %e A239304 1 %e A239304 1 2 %e A239304 3 1 2 %e A239304 4 2 1 3 %e A239304 2 5 4 1 3 %e A239304 2 5 6 3 1 4 %e A239304 Square array begins: %e A239304 1 1 3 4 2 2 %e A239304 2 1 2 5 5 2 %e A239304 2 1 4 6 3 2 %e A239304 3 1 3 7 6 2 %e A239304 3 1 5 8 4 2 %e A239304 4 1 4 9 7 2 %e A239304 Row 5 of A239303 is the vector (12,18,1,17,10), which corresponds to the following binary matrix: %e A239304 0 0 1 1 0 %e A239304 0 1 0 0 1 %e A239304 1 0 0 0 0 %e A239304 1 0 0 0 1 %e A239304 0 1 0 1 0 %e A239304 Interpreted as an adjacency matrix it describes the following graph, where each number is connected to its neighbors, and only the 2 is connected to itself: %e A239304 2 5 4 1 3 %e A239304 This is row 5 of the triangular array. %Y A239304 Cf. A239303, A028242, A084964, A168230, A152832. %K A239304 nonn,tabl %O A239304 1,3 %A A239304 _Tilman Piesk_, Mar 14 2014