A048668 -id:A048668 - cp's OEIS frontend

A048790 Array read by antidiagonals: T(n,k) = number of rooted n-dimensional polycubes with k cells, with no symmetries removed (n >= 1, k >= 1).

1, 1, 2, 1, 4, 3, 1, 6, 18, 4, 1, 8, 45, 76, 5, 1, 10, 84, 344, 315, 6, 1, 12, 135, 936, 2670, 1296, 7, 1, 14, 198, 1980, 10810, 20886, 5320, 8, 1, 16, 273, 3604, 30475, 127632, 164514, 21800, 9, 1, 18, 360, 5936, 69405, 483702, 1531180, 1303304, 89190, 10, 1

Offset: 1

Dan Hoey

			Array begins:
n\k 1..2...3.....4......5.......6........7........8........9.....10......11......12.......13
1 | 1..2...3.....4......5.......6........7........8........9.....10......11......12.......13
2 | 1..4..18....76....315....1296.....5320....21800....89190.364460.1487948.6070332.24750570
3 | 1..6..45...344...2670...20886...164514..1303304.10375830
4 | 1..8..84...936..10810..127632..1531180.18589840
5 | 1.10.135..1980..30475..483702..7847525
6 | 1.12.198..3604..69405.1386048.28403620
7 | 1.14.273..5936.137340.3307878
8 | 1.16.360..9104.246020
9 | 1.18.459.13236.409185

Dan Hoey, Bill Gosper and Richard C. Schroeppel, Discussions in Math-Fun Mailing list, circa Jul 13 1999.

R. C. Schroeppel, A few mathematical experiments

Rows give A048663-A048668, A094101. Columns give A094159-A094161. Cf. A094100.

More terms from Joshua Zucker, Aug 14 2006

Edited by N. J. A. Sloane, Sep 15 2008 at the suggestion of R. J. Mathar

A151833 Number of fixed 7-dimensional polycubes with n cells.

Original entry on oeis.org

1, 7, 91, 1484, 27468, 551313, 11710328, 259379101, 5933702467, 139272913892, 3338026689018, 81406063278113, 2014611366114053, 50486299825273271

Offset: 1

N. J. A. Sloane, Jul 12 2009

G. Aleksandrowicz and G. Barequet, Counting d-dimensional polycubes and nonrectangular planar polyominoes, Int. J. of Computational Geometry and Applications, 19 (2009), 215-229.
G. Aleksandrowicz and G. Barequet, Counting polycubes without the dimensionality curse, Discrete Mathematics, 309 (2009), 4576-4583.
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.
Gill Barequet, Solomon W. Golomb, and David A. Klarner, Polyominoes. (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, http://www.csun.edu/~ctoth/Handbook/chap14.pdf
R. Barequet, G. Barequet, and G. Rote, Formulae and growth rates of high-dimensional polycubes, Combinatorica, 30 (2010), 257-275.
S. Luther and S. Mertens, Counting lattice animals in high dimensions, Journal of Statistical Mechanics: Theory and Experiment, 2011 (9), 546-565.

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).

Cf. A001931, A048668, A151830, A151831, A151832, A151834, A151835.

A048668 = Cases[Import["https://oeis.org/A048668/b048668.txt", "Table"], {, }][[All, 2]];
a[n_] := A048668[[n]]/n;
Array[a, 14] (* Jean-François Alcover, Sep 12 2019 *)

a(n) = A048668(n)/n. - Jean-François Alcover, Sep 12 2019, after Andrew Howroyd in A048668.

More terms from Gadi Aleksandrowicz (gadial(AT)gmail.com), Mar 21 2010

a(11)-a(14) from Luther and Mertens by Gill Barequet, Jun 12 2011

cp's OEIS Frontend

A048790 Array read by antidiagonals: T(n,k) = number of rooted n-dimensional polycubes with k cells, with no symmetries removed (n >= 1, k >= 1).

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