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Number of fixed 9-dimensional polycubes with n cells.
6

%I #25 Jan 29 2023 09:45:03

%S 1,9,153,3309,81837,2205489,63113061,1887993993,58441956579,

%T 1858846428437,60445700665383,2001985304489169,67341781440810531,

%U 2295424989986481345

%N Number of fixed 9-dimensional polycubes with n cells.

%C a(1)-a(10) can be computed by formulas in Barequet et al. (2010). Luther and Mertens confirm these values (and add two more) by direct counting.

%H G. Aleksandrowicz and G. Barequet, <a href="https://doi.org/10.1142/S0218195909002927">Counting d-dimensional polycubes and nonrectangular planar polyominoes</a>, Int. J. of Computational Geometry and Applications, 19 (2009), 215-229.

%H Gill Barequet, Gil Ben-Shachar, and Martha Carolina Osegueda, <a href="http://www1.pub.informatik.uni-wuerzburg.de/eurocg2020/data/uploads/papers/eurocg20_paper_23.pdf">Applications of Concatenation Arguments to Polyominoes and Polycubes</a>, EuroCG '20, 36th European Workshop on Computational Geometry, (Würzburg, Germany, 16-18 March 2020).

%H Gill Barequet, Solomon W. Golomb, and David A. Klarner, Polyominoes; in: Handbook of Discrete and Computational Geometry, Chapman and Hall/CRC, 2017. (This is a revision, by G. Barequet, of the chapter of the same title originally written by the late D. A. Klarner for the first edition, and revised by the late S. W. Golomb for the second edition.) <a href="https://www.csun.edu/~ctoth/Handbook/chap14.pdf">Preprint</a>, 2016.

%H R. Barequet, G. Barequet, and G. Rote, <a href="https://doi.org/10.1007/s00493-010-2448-8">Formulae and growth rates of high-dimensional polycubes</a>, Combinatorica, 30 (2010), 257-275.

%H S. Luther and S. Mertens, <a href="https://doi.org/10.1088/1742-5468/2011/09/P09026">Counting lattice animals in high dimensions</a>, Journal of Statistical Mechanics: Theory and Experiment, 2011 (9), P09026.

%H Stephan Mertens, <a href="https://wasd.urz.uni-magdeburg.de/mertens/research/animals/">Lattice Animals</a>

%Y Cf. A001931, A151830, A151831, A151832, A151833, A151834.

%K nonn,more

%O 1,2

%A _N. J. A. Sloane_, Jul 12 2009

%E a(5)-a(12) from Luther and Mertens by _Gill Barequet_, Jun 12 2011

%E a(13)-a(14) from Mertens added by _Andrey Zabolotskiy_, Jan 29 2023