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 A309524 #11 Feb 16 2025 08:33:55 %S A309524 1,0,1,0,0,2,0,0,1,5,0,0,1,2,18,0,0,1,3,17,91,0,0,1,3,29,86,734,0,0,1, %T A309524 4,42,176,864,10030,0,0,1,4,64,309,2032,10243,248427 %N A309524 Triangle read by rows: T(n,k) is the number of simple connected graphs on n nodes with longest path having k nodes, (1 <= k <= n). %C A309524 Paths here are subgraphs that are isomorphic to a path graph and are measured by the number of vertices they contain rather than the number of edges. No vertex can appear more than once. %C A309524 Paths with three vertices exist in all connected graphs with at least three vertices. For n > 3, the star graph is the only graph in which longer paths are not possible. %H A309524 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LongestPath.html">Longest Path</a> %H A309524 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TraceableGraph.html">Traceable Graph</a> %e A309524 Triangle begins: %e A309524 1; %e A309524 0, 1; %e A309524 0, 0, 2; %e A309524 0, 0, 1, 5; %e A309524 0, 0, 1, 2, 18; %e A309524 0, 0, 1, 3, 17, 91; %e A309524 0, 0, 1, 3, 29, 86, 734; %e A309524 0, 0, 1, 4, 42, 176, 864, 10030; %e A309524 0, 0, 1, 4, 64, 309, 2032, 10243, 248427; %e A309524 ... %Y A309524 Row sums are A001349. %Y A309524 Right diagonal is A057864. %Y A309524 Cf. A325455 (circumference = longest cycle). %Y A309524 Cf. A307457. %K A309524 nonn,tabl,more %O A309524 1,6 %A A309524 _Andrew Howroyd_, Sep 06 2019