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A118356
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Number of clusters with n vertices, n-1 edges and zero contacts on the simple cubic lattice.
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6
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1, 3, 15, 83, 486, 2967, 18748, 121725, 807381, 5447203, 37264974, 257896500, 1802312605, 12701190885, 90157130289, 644022007040, 4626159163233
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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 (barequet(AT)cs.technion.ac.il), May 25 2011
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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.
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LINKS
| 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
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CROSSREFS
| Cf. A066158 (fixed tree-like polyominoes), A191094 - A191098 (fixed tree-like polycubes in 4, 5, 6, 7, and 8 dimensions, resp.)
Sequence in context: A192662 A052451 A026019 * A074552 A193658 A195885
Adjacent sequences: A118353 A118354 A118355 * A118357 A118358 A118359
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KEYWORD
| nonn,more
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AUTHOR
| R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 14 2006
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EXTENSIONS
| a(1)=1 added by Gill Barequet (barequet(AT)cs.technion.ac.il), May 25 2011
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