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%I #13 Aug 13 2017 16:30:17
%S 1,0,1,2,5,29,188,2481,52499,1857651,104392105
%N Number of graphs with n nodes that are Hamiltonian and have no induced subgraph isomorphic to K_4.
%C K_4 is the complete graph on four vertices.
%H Travis Hoppe and Anna Petrone, <a href="https://github.com/thoppe/Encyclopedia-of-Finite-Graphs">Encyclopedia of Finite Graphs</a>
%H T. Hoppe and A. Petrone, <a href="http://arxiv.org/abs/1408.3644">Integer sequence discovery from small graphs</a>, arXiv preprint arXiv:1408.3644, 2014
%H F. Hüffner, <a href="https://github.com/falk-hueffner/tinygraph">tinygraph</a>, software for generating integer sequences based on graph properties, version 4361e42
%Y Cf. A003216 (Hamiltonian graphs), A079574 (connected K_4 free graphs).
%K nonn,more
%O 1,4
%A _Travis Hoppe_ and _Anna Petrone_, Jun 02 2014
%E a(11) added using tinygraph by _Falk Hüffner_, Aug 13 2017