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A066158
Number of fixed polyominoes with n cells and tree-like structure.
11
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
1,2
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.).
Sequence in context: A294159 A000778 A006725 * A148456 A148457 A182881
KEYWORD
nonn
AUTHOR
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.
STATUS
approved