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Number of connected diamond-free graphs on n nodes.
12

%I #16 Jan 15 2016 11:30:15

%S 1,1,2,4,11,39,165,967,7684,87012,1410465,32640019

%N Number of connected diamond-free graphs on n nodes.

%C An equivalent definition: Number of simple connected graphs with n nodes that are have no subgraph isomorphic to the diamond graph or the complete graph K_4. This is the same because a graph contains a diamond as a subgraph iff it contains a diamond or K_4 as induced subgraph. - _Falk Hüffner_, Jan 11 2015

%H Travis Hoppe and Anna Petrone, <a href="https://github.com/thoppe/Encyclopedia-of-Finite-Graphs">Encyclopedia of Finite Graphs</a>

%H Falk Hüffner, <a href="https://github.com/falk-hueffner/tinygraph">tinygraph</a>, software for generating integer sequences based on graph properties, version ece94ef.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DiamondGraph.html">Diamond Graph</a>

%Y Cf. A077269 (connected squarefree graphs).

%Y Cf. also A242790 (diamond free graphs), A079574 (K_4 free graphs).

%K nonn,more

%O 1,3

%A _Travis Hoppe_ and _Anna Petrone_, May 22 2014

%E Entry revised by _N. J. A. Sloane_, Jan 11 2016

%E a(11) and a(12) added using tinygraph by _Falk Hüffner_, Jan 15 2016