A066158 Number of fixed polyominoes with n cells and tree-like structure.

1, 2, 6, 18, 55, 174, 570, 1908, 6473, 22202, 76886, 268352, 942651, 3329608, 11817582, 42120340, 150682450, 540832274, 1946892842, 7027047848, 25424079339, 92185846608, 334925007128, 1219054432490, 4444545298879, 16229462702152, 59347661054364

Offset: 1

Author

Jan Kristian Haugland, Dec 13 2001

Keywords

• nonn
• changed

Comments

Computed by a modified version of the program used for A065068.

Aleksandrowicz and Barequet (2011) confirm first 27 terms. - 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.
• N. Madras, C. E. Soteros, S. G. Whittington, J. L. Martin, M. F. Sykes et al., The free energy of a collapsing branched polymer, J. Phys. A: Math. Gen. 23 (1990) 5327-5350.

Links

• I. Jensen, Table of n, a(n) for n = 1..44 [From the arXiv paper]
• 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).
• I. Jensen, Enumerations of lattice animals and trees, J. Stat. Phys. 103 (3-4) (2001) 865-881, Table II.
• I. Jensen, Enumerations of lattice animals and trees, arXiv:cond-mat/0007239.

Crossrefs

Cf. A001168 (fixed polyominoes), A019441 (coefficients of g.f. related to this sequence), A118356, A191094, A191095, A191096, A191097, A191098 (fixed tree-like polycubes in 3, 4, 5, 6, 7, and 8 dimensions, resp.).

Extensions

Added a(18) and a(19) from Madras et al. - R. J. Mathar, Apr 08 2006

Terms from a(20) on added by N. J. A. Sloane, Nov 05 2008, from the Jensen paper.