cp's OEIS Frontend

A151832 Number of fixed 6-dimensional polycubes with n cells.

%I A151832 #56 Jun 27 2025 04:25:59
%S A151832 1,6,66,901,13881,231008,4057660,74174927,1398295989,27012396022,
%T A151832 532327974882,10665521789203,216696065279573,4455636282185802,
%U A151832 92567760074841818
%N A151832 Number of fixed 6-dimensional polycubes with n cells.
%D A151832 Anthony J. Guttmann, editor. Polygons, Polyominoes and Polycubes, volume 775 of Lecture Notes in Physics. Springer-Verlag, Heidelberg, 2009.
%H A151832 J. Adler, Y. Meir, A. B. Harris, A. Aharony, and J. A. M. S. Duarté, <a href="https://doi.org/10.1103/PhysRevB.38.4941">Series study of random animals in general dimensions</a>, Physical Review B, 38 (1988) 4941.
%H A151832 Gadi Aleksandrowicz and Gill 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 A151832 Gadi Aleksandrowicz and Gill 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 A151832 Gadi Aleksandrowicz and Gill 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 A151832 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 A151832 Gill Barequet, Solomon W. Golomb, and David A. Klarner, <a href="https://www.csun.edu/~ctoth/Handbook/chap14.pdf">Polyominoes</a>. (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.) Preprint, 2016.
%H A151832 Ronnie Barequet, Gill Barequet, and Günter Rote, <a href="https://doi.org/10.1007/s00493-010-2448-8">Formulae and growth rates of high-dimensional polycubes</a>, Combinatorica 30, 257-275 (2010).
%H A151832 D. S. Gaunt and P. J. Peard, <a href="https://doi.org/10.1088/0305-4470/33/42/304">1/d-expansions for the free energy of weakly embedded site animal models of branched polymers</a>, Journal of Physics A: Mathematical and General, 33 (2000) 7515-7539.
%H A151832 Hsiao-Ping Hsu, Walter Nadler, and Peter Grassberger, <a href="https://doi.org/10.1016/j.cpc.2005.03.027">Statistics of lattice animals</a>, Computer Physics Communications, 169 (2005) 114-116.
%H A151832 Iwan Jensen, <a href="https://doi.org/10.1023/A:1004855020556">Enumerations of lattice animals and trees</a>, Journal of Statistical Physics, 102(3/4) (2001) 865-881.
%H A151832 Sebastian Luther and Stephan 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), 546-565. See Table 2 for the terms (but beware of the incorrect a(13)!) or Table 3 for the formulas.
%H A151832 Sebastian Luther and Stephan Mertens, <a href="https://arxiv.org/abs/1106.1078">Counting lattice animals in high dimensions</a>, arXiv:1106.1078 [cond-mat.stat-mech], 2011.
%H A151832 Stephan Mertens and Markus E. Lautenbacher, <a href="https://doi.org/10.1007/BF01060088">Counting lattice animals: A parallel attack</a>, J. Stat. Phys. 66 (1992) 669.
%F A151832 a(n) = A048667(n)/n. - _Jean-François Alcover_, Sep 12 2019, after _Andrew Howroyd_ in A048667.
%t A151832 A048667 = Cases[Import["https://oeis.org/A048667/b048667.txt", "Table"], {_, _}][[All, 2]];
%t A151832 a[n_] := A048667[[n]]/n;
%t A151832 Array[a, 15] (* _Jean-François Alcover_, Sep 12 2019 *)
%Y A151832 Cf. A001931, A048667, A151830, A151831, A151833, A151834, A151835.
%K A151832 nonn,more
%O A151832 1,2
%A A151832 _N. J. A. Sloane_, Jul 12 2009
%E A151832 a(10) from Gadi Aleksandrowicz (gadial(AT)gmail.com), Mar 21 2010
%E A151832 a(11)-a(15) from Luther and Mertens by _Gill Barequet_, Jun 12 2011
%E A151832 a(13) corrected by _M. F. Hasler_, Jun 26 2025