A066158
Number of fixed polyominoes with n cells and tree-like structure.
Original entry on oeis.org
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
- 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.
- 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.
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.).
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.
A191094
Number of n-cell fixed tree-like polycubes in 4 dimensions.
Original entry on oeis.org
1, 4, 28, 228, 2018, 18892, 184400, 1857856, 19189675, 202214452
Offset: 1
- 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.
Cf.
A066158 (fixed tree-like polyominoes),
A118356,
A191095,
A191096,
A191097,
A191098 (fixed tree-like polycubes in 3, 5, 6, 7, and 8 dimensions, resp.).
A191095
Number of n-cell fixed tree-like polycubes in 5 dimensions.
Original entry on oeis.org
1, 5, 45, 485, 5775, 73437, 979335, 13536225, 192393410, 2796392165
Offset: 1
- 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.
Cf.
A066158 (fixed tree-like polyominoes),
A118356,
A191094,
A191096,
A191097,
A191098 (fixed tree-like polycubes in 3, 4, 6, 7, and 8 dimensions, resp.).
A191096
Number of n-cell fixed tree-like polycubes in 6 dimensions.
Original entry on oeis.org
1, 6, 66, 886, 13281, 213978, 3630090, 64012932
Offset: 1
- 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.
Cf.
A066158 (fixed tree-like polyominoes),
A118356,
A191094,
A191095,
A191097,
A191098 (fixed tree-like polycubes in 3, 4, 5, 7, and 8 dimensions, resp.).
A191097
Number of n-cell fixed tree-like polycubes in 7 dimensions.
Original entry on oeis.org
1, 7, 91, 1463, 26460, 516691, 10654378
Offset: 1
- 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.
Cf.
A066158 (fixed tree-like polyominoes),
A118356,
A191094,
A191095,
A191096,
A191098 (fixed tree-like polycubes in 3, 4, 5, 6, and 8 dimensions, resp.).
A191098
Number of n-cell fixed tree-like polycubes in 8 dimensions.
Original entry on oeis.org
1, 8, 120, 2248, 47636, 1088017, 26424957
Offset: 1
- 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.
Cf.
A066158 (fixed tree-like polyominoes),
A118356,
A191094,
A191095,
A191096,
A191097 (fixed tree-like polycubes in 3, 4, 5, 6, and 7 dimensions, resp.).
A304196
Number of free tree-like polycubes of size n in three dimensions.
Original entry on oeis.org
1, 1, 2, 6, 21, 91, 484, 2817, 17788, 116741, 788081, 5414701, 37703459, 265182187
Offset: 1
- Alexandre Blondin Massé, Julien de Carufel, Alain Goupil, and Maxime Samson, Fully-leafed tree-like polyominoes and polycubes, In Combinatorial algorithms, volume 10765 of Lecture Notes of Computer Science, 28th International workshop, IWOCA 2017, Newcastle, NSW, Australia, Springer, 2018.
Cf.
A118356 (fixed tree-like 3d-polycubes),
A304198 (free tree-like 4d-polycubes),
A131482 (free tree-like polyominoes).
A363199
Number of free tree-like polycubes of size n, identifying rotations but not reflections.
Original entry on oeis.org
1, 1, 2, 7, 27, 138, 822, 5154, 33880, 227495, 1554266, 10749089, 75106906
Offset: 1
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