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A118356
Number of clusters with n vertices, n-1 edges and zero contacts on the simple cubic lattice.
8
1, 3, 15, 83, 486, 2967, 18748, 121725, 807381, 5447203, 37264974, 257896500, 1802312605, 12701190885, 90157130289, 644022007040, 4626159163233
OFFSET
1,2
COMMENTS
a(n)<=A001931(n) due to the "no-contact" restriction.
An alternative wording for a(n) is the number of n-cell fixed tree-like polycubes in 3 dimensions. - Gill Barequet, May 25 2011
REFERENCES
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.
LINKS
Gill Barequet, Gil Ben-Shachar, Martha Carolina Osegueda, Applications of Concatenation Arguments to Polyominoes and Polycubes, EuroCG '20, 36th European Workshop on Computational Geometry, (Würzburg, Germany, 16-18 March 2020).
N. Madras, C. E. Soteros, S. G. Whittington, J. L. Martin et al., The free energy of a collapsing branched polymer, J Phys A: Math Gen 23 (1990) 5327-5350
CROSSREFS
Cf. A066158 (fixed tree-like polyominoes), A191094, A191095, A191096, A191097, A191098 (fixed tree-like polycubes in 4, 5, 6, 7, and 8 dimensions, resp.).
Sequence in context: A052451 A026019 A354660 * A074552 A193658 A195885
KEYWORD
nonn,more
AUTHOR
R. J. Mathar, May 14 2006
EXTENSIONS
a(1)=1 added by Gill Barequet, May 25 2011
STATUS
approved