

A118356


Number of clusters with n vertices, n1 edges and zero contacts on the simple cubic lattice.


7



1, 3, 15, 83, 486, 2967, 18748, 121725, 807381, 5447203, 37264974, 257896500, 1802312605, 12701190885, 90157130289, 644022007040, 4626159163233
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OFFSET

1,2


COMMENTS

a(n)<=A001931(n) due to the "nocontact" restriction.
An alternative wording for a(n) is the number of ncell fixed treelike 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, SpringerVerlag, 9099, May 2011.


LINKS

Table of n, a(n) for n=1..17.
Gill Barequet, Gil BenShachar, Martha Carolina Osegueda, Applications of Concatenation Arguments to Polyominoes and Polycubes, EuroCG '20, 36th European Workshop on Computational Geometry, (Würzburg, Germany, 1618 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) 53275350


CROSSREFS

Cf. A066158 (fixed treelike polyominoes), A191094, A191095, A191096, A191097, A191098 (fixed treelike polycubes in 4, 5, 6, 7, and 8 dimensions, resp.).
Sequence in context: A213096 A052451 A026019 * A074552 A193658 A195885
Adjacent sequences: A118353 A118354 A118355 * A118357 A118358 A118359


KEYWORD

nonn,more


AUTHOR

R. J. Mathar, May 14 2006


EXTENSIONS

a(1)=1 added by Gill Barequet, May 25 2011


STATUS

approved



