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 A328060 #37 Jan 14 2025 16:29:14
%S A328060 1,1,0,0,0,1,1,5,19,123,871,8304,92539,1210044,17860267,293210063,
%T A328060 5277557739,103177250918,2174556695546
%N A328060 Number of bipartite Laman graphs on n vertices.
%C A328060 All the Laman graphs (in other words, minimally rigid graphs) can be constructed by the inductive Henneberg construction, i.e., a sequence of Henneberg steps starting from K_2. A new vertex added by a Henneberg move is connected with two or three of the previously existing vertices. Hence, the chromatic number of a Laman graph can be 2, 3 or 4. One can hypothesize that the set of 3-chromatic Laman graphs is the largest and that bipartite graphs are relatively rare. The first nontrivial bipartite Laman graph is K_{3,3}. An infinite sequence of such graphs can be obtained from K_{3,3} by Henneberg moves of the first type (i.e., adding a vertex and connecting it with two of the existing vertices from the one part).
%H A328060 L. Henneberg, <a href="https://archive.org/details/diegraphischest00henngoog">Die graphische Statik der starren Systeme</a>, Leipzig, 1911.
%H A328060 F. Hüffner, <a href="https://github.com/falk-hueffner/tinygraph">tinygraph</a>, software for generating integer sequences based on graph properties.
%H A328060 Christoph Koutschan, <a href="https://oeis.org/A227117/a227117_2.txt">Mathematica program</a> for generating a list of non-isomorphic Laman graphs on n vertices.
%H A328060 G. Laman, <a href="http://www.wisdom.weizmann.ac.il/~vision/courses/2010_2/papers/OnGraphsAndRigidity.pdf">On Graphs and Rigidity of Planar Skeletal Structures</a>, J. Engineering Mathematics, Vol. 4, No. 4, 1970, pp. 331-340.
%H A328060 Martin Larsson, <a href="https://github.com/martinkjlarsson/nauty-laman-plugin">C program</a>
%H A328060 A. Nixon and E. Ross, <a href="https://arxiv.org/abs/1203.6623">One brick at a time: a survey of inductive constructions in rigidity theory</a>, arXiv:1203.6623 [math.MG], 2012-2013.
%H A328060 Wikipedia, <a href="https://en.wikipedia.org/wiki/Laman_graph">Laman graph</a>
%t A328060 Table[Length[
%t A328060 Select[LamanGraphs[n],
%t A328060 BipartiteGraphQ[AdjacencyGraph[G2Mat[#]]] &]], {n, 6, 9}] (* using the program by Christoph Koutschan for generating Laman graphs, see A227117 *)
%Y A328060 Cf. A227117, A273468, A306420, A328061, A371901.
%K A328060 nonn,more
%O A328060 1,8
%A A328060 _Vsevolod Voronov_, Oct 03 2019
%E A328060 a(13)-a(15) added using tinygraph by _Falk Hüffner_, Oct 20 2019
%E A328060 a(16)-a(17) added by _Martin Larsson_, Dec 21 2020
%E A328060 a(18)-a(19) from _Martin Larsson_ added by _Max Alekseyev_, Jan 14 2025