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 A385156 #29 Aug 17 2025 19:11:36 %S A385156 0,0,0,0,1,0,0,0,0,22,310,4177 %N A385156 The number of undirected, simple, unlabeled graphs G on n vertices which are prime, not split, and do not contain a vertex of degree 1 in G or in the complement of G, and has no induced P5 in G or in the complement of G. %C A385156 Here, "prime" means with respect to modular decomposition (see link). A P5 is a path on 5 vertices. A split graph is a graph whose vertices can be partitioned into a clique and an independent set. Related to conjectures in the referenced paper. %D A385156 Maria Chudnovsky and Peter Maceli, "Simplicial Vertices in Graphs with no Induced Four-Edge Path or Four-Edge Antipath, and the H6-Conjecture," Journal of Graph Theory, vol 76, no 4, (2014). %H A385156 Maria Chudnovsky and Peter Maceli, <a href="https://arxiv.org/abs/1302.0404">Simplicial Vertices in Graphs with no Induced Four-Edge Path or Four-Edge Antipath, and the H6-Conjecture</a>, arXiv:1302.0404 [math.CO], 2013. %H A385156 House of Graphs, <a href="https://houseofgraphs.org/graphs/53727">One of the 22 graphs on 10 vertices</a>. %H A385156 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a385/A385156.java">Java program</a> (github) %H A385156 Wikipedia, <a href="https://en.wikipedia.org/wiki/Modular_decomposition">Modular decomposition</a>. %e A385156 a(5) = 1 is the C5. %e A385156 One of the examples of a(10) = 22 is available in the links. %Y A385156 Cf. A385697 (when split graph condition is dropped). %K A385156 nonn,more %O A385156 1,10 %A A385156 _Jim Nastos_ and _Clara Elliott_, Jul 22 2025 %E A385156 a(11)-a(12) from _Sean A. Irvine_, Aug 17 2025