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 A363363 #6 Jun 02 2023 08:39:26
%S A363363 0,0,0,0,0,4,26,209,1513,12145
%N A363363 Number of connected unlabeled n-node graphs G that are not weakly pancyclic, i.e., there exists an integer k such that G contains a cycle that is longer than k and a cycle that is shorter than k but no cycle of length k.
%H A363363 Stephan Brandt, Ralph Faudree, and Wayne Goddard, <a href="https://doi.org/10.1002/(SICI)1097-0118(199803)27:3%3C141::AID-JGT3%3E3.0.CO;2-O">Weakly pancyclic graphs</a>, Journal of Graph Theory 27 (1998), 141-176.
%F A363363 a(n) = A001349(n) - A363362(n).
%F A363363 a(n) = 0 for n <= 5, because all graphs on at most 5 nodes are weakly pancyclic.
%e A363363 There are a(6) = 4 not weakly pancyclic graphs on 6 nodes (all of them connected):
%e A363363 a cycle of length 6 with one additional edge (two different graphs);
%e A363363 the complete bipartite graph K_{3,3} with one edge removed;
%e A363363 K_{3,3}.
%Y A363363 Cf. A001349, A363362, A363364.
%K A363363 nonn,more
%O A363363 1,6
%A A363363 _Pontus von Brömssen_, May 29 2023