cp's OEIS Frontend

A001931 Number of fixed 3-dimensional polycubes with n cells; lattice animals in the simple cubic lattice (6 nearest neighbors), face-connected cubes.

%I A001931 M2996 N1213 #101 Feb 08 2024 01:41:05
%S A001931 1,3,15,86,534,3481,23502,162913,1152870,8294738,60494549,446205905,
%T A001931 3322769321,24946773111,188625900446,1435074454755,10977812452428,
%U A001931 84384157287999,651459315795897,5049008190434659,39269513463794006,306405169166373418
%N A001931 Number of fixed 3-dimensional polycubes with n cells; lattice animals in the simple cubic lattice (6 nearest neighbors), face-connected cubes.
%C A001931 This gives the number of polycubes up to translation (but not rotation or reflection). - _Charles R Greathouse IV_, Oct 08 2013
%D A001931 W. F. Lunnon, Symmetry of cubical and general polyominoes, pp. 101-108 of R. C. Read, editor, Graph Theory and Computing. Academic Press, NY, 1972.
%D A001931 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001931 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001931 G. Aleksandrowicz and G. Barequet, <a href="http://dx.doi.org/10.1007/11809678_44">Counting d-dimensional polycubes and nonrectangular planar polyominoes</a>, Computing and Combinatorics, 12th Annual International Conference, COCOON 2006, Taipei, Taiwan, August 15-18, 2006, pp. 418-427.
%H A001931 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 A001931 A. Asinowski, G. Barequet, and Y. Zheng, <a href="https://doi.org/0.1137/1.9781611975031.6">Polycubes with small perimeter defect</a>, Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, (2018).
%H A001931 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 A001931 Gill Barequet, Solomon W. Golomb, and David A. Klarner, <a href="http://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 A001931 Andrew R. Conway, <a href="https://dx.doi.org/10.1088/1751-8121/aa8120">The design of efficient dynamic programming and transfer matrix enumeration algorithms</a>, Journal of Physics A: Mathematical and Theoretical, 2 August 2017. For another version see <a href="https://arxiv.org/abs/1610.09806">arXiv</a>, arXiv:1610.09806 [math.CO], 2016-2017.
%H A001931 Stanley Dodds, <a href="/A001931/a001931.cs.txt">C# program for this sequence</a>
%H A001931 Kevin L. Gong, <a href="http://kevingong.com/Polyominoes/Enumeration.html">Polyominoes Home Page</a>
%H A001931 S. Luther and S. Mertens, <a href="http://arxiv.org/abs/1106.1078">Counting lattice animals in high dimensions</a>, Journal of Statistical Mechanics: Theory and Experiment, 2011 (9), 546-565; arXiv:1106.1078 [cond-mat.stat-mech], 2011.
%H A001931 S. Mertens, <a href="http://dx.doi.org/10.1007/BF01026565">Lattice animals: a fast enumeration algorithm and new perimeter polynomials</a>, J. Stat. Phys. 58 (5-6) (1990) 1095-1108, Table 1.
%H A001931 H. Redelmeier, <a href="/A006770/a006770.pdf">Emails to N. J. A. Sloane, 1991</a>
%H A001931 Phillip Thompson, <a href="/A001931/a001931.txt">rust port of Dodds's C# program</a>
%Y A001931 Cf. A000162, A001420, A038119 (free), A151830, A151832, A151833, A151834, A151835.
%Y A001931 32nd row of A366767.
%K A001931 nonn,nice,more
%O A001931 1,2
%A A001931 _N. J. A. Sloane_
%E A001931 Edited by _Arun Giridhar_, Feb 14 2011
%E A001931 a(17) from _Achim Flammenkamp_, Feb 15 1999
%E A001931 a(18) from the Aleksandrowicz and Barequet paper (_N. J. A. Sloane_, Jul 09 2009)
%E A001931 a(19) from Luther and Mertens by _Gill Barequet_, Jun 12 2011
%E A001931 a(20) from _Stanley Dodds_, Aug 03 2023
%E A001931 a(21)-a(22) (using Dodds's algorithm) from _Phillip Thompson_, Feb 07 2024