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 A382755 #5 Apr 06 2025 15:03:55 %S A382755 0,0,0,1,0,1,1,3,1,3,3,7,0,1,1,3,1,3,3,7,1,3,3,11,12,13,13,15,1,3,12, %T A382755 13,3,11,13,15,3,7,13,15,13,15,30,31,1,12,3,13,3,13,11,15,3,13,7,15, %U A382755 13,30,15,31,3,13,13,30,7,15,15,31,11,15,15,31,15,31,31,63 %N A382755 Irregular triangle read by rows: Let k encode the edges of an n-vertex graph by taking edges (u,v), with u < v, in lexicographic order ((0,1), ..., (0,n-1), (1,2), ..., (1,n-1), ..., (n-1,n)) and adding each edge to the graph if the corresponding binary digit of k (starting with the least significant digit) is 1. T(n,k) is the smallest nonnegative integer that encodes the same unlabeled n-vertex graph as k, 0 <= k < n*(n-1)/2. %C A382755 In the encoding given by A382754, the code of the graph corresponding to T(n,k) is 2^(n*(n-1)/2) + T(n,k) if n > 0. %C A382755 The first case where a row is not an initial segment of the next row is T(4,11) = 11 != 7 = T(5,11). %F A382755 T(n,k) <= k with equality if and only if 2^(n*(n-1)/2) + k is in A382754. %e A382755 Triangle begins: %e A382755 0; %e A382755 0; %e A382755 0, 1; %e A382755 0, 1, 1, 3, 1, 3, 3, 7; %e A382755 ... %e A382755 For n = 5, k = 11, 11 is 1011 in binary, which encodes the 5-vertex graph with edges (0,1), (0,2), and (0,4) (3 being an isolated vertex). The smallest code for an isomorphic graph is obtained by substituting the edge (0,3) for (0,4), resulting in the code 111 in binary, i.e., T(5,11) = 7. %Y A382755 Cf. A382281, A382754. %K A382755 nonn,tabf %O A382755 0,8 %A A382755 _Pontus von Brömssen_, Apr 04 2025