cp's OEIS Frontend

A151834 Number of fixed 8-dimensional polycubes with n cells.

%I A151834 #24 Jan 29 2023 09:44:58
%S A151834 1,8,120,2276,49204,1156688,28831384,750455268,20196669078,
%T A151834 558157620384,15762232227968,453181069339660,13228272325440164,
%U A151834 391166062869849024
%N A151834 Number of fixed 8-dimensional polycubes with n cells.
%C A151834 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 A151834 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 A151834 G. Aleksandrowicz and G. Barequet, <a href="https://doi.org/10.1016/j.disc.2009.02.023">Counting polycubes without the dimensionality curse</a>, Discrete Mathematics, 309 (2009), 4576-4583.
%H A151834 G. Aleksandrowicz and G. Barequet, <a href="https://doi.org/10.1007/978-3-642-21204-8_13">Parallel enumeration of lattice animals</a>, Proc. 5th Int. Frontiers of Algorithmics Workshop, Zhejiang, China, Lecture Notes in Computer Science, 6681, Springer-Verlag, 90-99, May 2011.
%H A151834 Gill Barequet, Gil Ben-Shachar, 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 A151834 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 A151834 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 A151834 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 A151834 Stephan Mertens, <a href="https://wasd.urz.uni-magdeburg.de/mertens/research/animals/">Lattice Animals</a>
%Y A151834 Cf. A001931, A151830, A151831, A151832, A151833, A151835.
%K A151834 nonn,more
%O A151834 1,2
%A A151834 _N. J. A. Sloane_, Jul 12 2009
%E A151834 More terms from Gadi Aleksandrowicz (gadial(AT)gmail.com), Mar 21 2010
%E A151834 a(9)-a(12) from Luther and Mertens by _Gill Barequet_, Jun 12 2011
%E A151834 a(13)-a(14) from Mertens added by _Andrey Zabolotskiy_, Jan 29 2023