A118356 Number of clusters with n vertices, n-1 edges and zero contacts on the simple cubic lattice.

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

Table of n, a(n) for n=1..17.

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

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