A001207 Number of fixed hexagonal polyominoes with n cells. (Formerly M2897 N1162)

1, 3, 11, 44, 186, 814, 3652, 16689, 77359, 362671, 1716033, 8182213, 39267086, 189492795, 918837374, 4474080844, 21866153748, 107217298977, 527266673134, 2599804551168, 12849503756579, 63646233127758, 315876691291677, 1570540515980274, 7821755377244303, 39014584984477092, 194880246951838595, 974725768600891269, 4881251640514912341, 24472502362094874818, 122826412768568196148, 617080993446201431307, 3103152024451536273288, 15618892303340118758816, 78679501136505611375745

Offset

1,2

Comments

The Voege-Guttmann paper extends the series to n=35. - Markus Voege (markus.voege(AT)inria.fr), Mar 25 2004

References

A. J. Guttmann, ed., Polygons, Polyominoes and Polycubes, Springer, 2009, p. 477. (Table 16.9 has 46 terms of this sequence.)

W. F. Lunnon, Counting hexagonal and triangular polyominoes, pp. 87-100 of R. C. Read, editor, Graph Theory and Computing. Academic Press, NY, 1972.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..46 (from reference by A. J. Guttmann)

Moa Apagodu, Counting hexagonal lattice animals, arXiv:math/0202295 [math.CO], 2002-2009.

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.

M. Bousquet-Mélou and A. Rechnitzer, Lattice animals and heaps of dimers, Discrete Mathematics, Volume 258, Issues 1-3, 6 December 2002, Pages 235-274.

Greg Malen, Érika Roldán, and Rosemberg Toalá-Enríquez, Extremal {p, q}-Animals, Ann. Comb. (2023), p. 3.

Stephan Mertens, Markus E. Lautenbacher, Counting lattice animals: a parallel attack, J. Statist. Phys. 66 (1992), no. 1-2, 669-678.

H. Redelmeier, Emails to N. J. A. Sloane, 1991

M. F. Sykes, M. Glen. Percolation processes in two dimensions. I. Low-density series expansions, J. Phys A 9 (1) (1976) 87.

Markus Voege and Anthony J. Guttmann, On the number of hexagonal polyominoes, Theoretical Computer Sciences, 307(2) (2003), 433-453.

Crossrefs

Cf. A000228 (free), A006535 (one-sided).

Sequence in context: A167013 A121220 A068091 * A319156 A026887 A151106

Adjacent sequences: A001204 A001205 A001206 * A001208 A001209 A001210

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

3 more terms and reference from Achim Flammenkamp, Feb 15 1999

More terms from Markus Voege (markus.voege(AT)inria.fr), Mar 25 2004

Status

approved