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

1,2

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.

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.

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.

Example

Unlike A006725, in this sequence cells can touch at corners. Accordingly, the sequences agree up to n=6, but a(7) = 570 = A006725(7) + 4 because this sequence includes the 4 rotations of this polyomino:
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Crossrefs

Cf. A001168 (all 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.), A066331 (polyhexes), A308409 (bond trees), A182644 (unbranched), A006725 (no corner touching), A131482 (free).

Sequence in context: A294159 A000778 A006725 * A148456 A148457 A182881

Adjacent sequences: A066155 A066156 A066157 * A066159 A066160 A066161

Keyword

nonn

Author

Jan Kristian Haugland, Dec 13 2001

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