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%I #17 Jul 03 2020 06:56:27
%S 1,3,15,83,486,2967,18748,121725,807381,5447203,37264974,257896500,
%T 1802312605,12701190885,90157130289,644022007040,4626159163233
%N Number of clusters with n vertices, n-1 edges and zero contacts on the simple cubic lattice.
%C a(n)<=A001931(n) due to the "no-contact" restriction.
%C An alternative wording for a(n) is the number of n-cell fixed tree-like polycubes in 3 dimensions. - _Gill Barequet_, May 25 2011
%D G. Aleksandrowicz and G. Barequet, Parallel enumeration of lattice animals, Proc. 5th Int. Frontiers of Algorithmics Workshop, Zhejiang, China, Lecture Notes in Computer Science, 6681, Springer-Verlag, 90-99, May 2011.
%H Gill Barequet, Gil Ben-Shachar, Martha Carolina Osegueda, <a href="http://www1.pub.informatik.uni-wuerzburg.de/eurocg2020/data/uploads/papers/eurocg20_paper_23.pdf">Applications of Concatenation Arguments to Polyominoes and Polycubes</a>, EuroCG '20, 36th European Workshop on Computational Geometry, (Würzburg, Germany, 16-18 March 2020).
%H N. Madras, C. E. Soteros, S. G. Whittington, J. L. Martin et al., <a href="http://dx.doi.org/10.1088/0305-4470/23/22/021">The free energy of a collapsing branched polymer</a>, J Phys A: Math Gen 23 (1990) 5327-5350
%Y Cf. A066158 (fixed tree-like polyominoes), A191094, A191095, A191096, A191097, A191098 (fixed tree-like polycubes in 4, 5, 6, 7, and 8 dimensions, resp.).
%K nonn,more
%O 1,2
%A _R. J. Mathar_, May 14 2006
%E a(1)=1 added by _Gill Barequet_, May 25 2011
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