%I #4 Apr 19 2016 01:07:36
%S 1,3,81,1594323,12157665459056928801
%N a(n)=3^((3^n - 1)/2).
%C Number of partitions into "bus routes" of the graph G_{n+1} defined below.
%H Author?, <a href="http://image.myany.jp/org/6c511f3698cf6db33d63d6450f331344.jpg">Mitsumata tree</a>
%e .........|..................G_1
%e ****
%e .......__|__................G_2
%e .........|
%e ****
%e .__|_____|_____|__..........G_3
%e ...|.....|.....|
%e .........|
%e .......__|__
%e .........|
%e ****.
%e ..._|_........._|_..........G_4
%e _|__|_____|_____|__|_
%e .|._|_....|...._|_.|
%e ....|.....|.....|
%e ......_|__|__|_
%e .......|._|_.|
%e ..........|
%e ****
%e G_1 = o---. = rooted tree with one edge and one leaf node. For n > 0, G_{n+1} is obtained from G_n by splitting each leaf node into three.
%Y Cf. A131709
%K nonn,easy
%O 0,2
%A _Yasutoshi Kohmoto_, Jan 09 2008
%E Edited by _N. J. A. Sloane_, Jan 29 2008
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