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Number of asymmetric equicolorable (unrooted) trees with 2*n vertices.
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%I #21 Jul 25 2019 04:34:17

%S 0,0,0,1,4,19,84,378,1727,8126,39055,191902,960681

%N Number of asymmetric equicolorable (unrooted) trees with 2*n vertices.

%C Any tree with 2n vertices is a bipartite graph with s vertices in one part and t vertices in the other part, where s <= t and s + t = 2n. We count trees with s = t = n, and which are asymmetric, that is, their only automorphism is the identity automorphism. These are also called identity trees.

%D R. C. Read and R. J. Wilson, Atlas of Graphs, Oxford Science Publications, Clarendon Press, OUP, 2004.

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

%H Austin Mohr, <a href="http://austinmohr.com/home/?page_id=1422">Unlabeled Trees</a>.

%e a(3) = 0 because there are six trees with 6 vertices, but only three of these have s = t = n = 3, and none of these three is asymmetric. The fourth term a(4) = 1 because there are nine trees with 8 vertices with s = t = n = 4 but only 1 is asymmetric, namely tree T46. See "Atlas of Graphs", page 65.

%Y Cf. A119856 (equicolorable trees with 2n vertices), A000220 (asymmetric trees with n vertices).

%K nonn,more

%O 1,5

%A _John P. McSorley_, Aug 08 2017

%E a(10)-a(13) added using tinygraph by _Falk Hüffner_, Jul 25 2019