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A118356 Number of clusters with n vertices, n-1 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 (list; graph; refs; listen; history; text; internal format)



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


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.


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, (W├╝rzburg, 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


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: A213096 A052451 A026019 * A074552 A193658 A195885

Adjacent sequences:  A118353 A118354 A118355 * A118357 A118358 A118359




R. J. Mathar, May 14 2006


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



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Last modified March 4 10:48 EST 2021. Contains 341791 sequences. (Running on oeis4.)