0,4

a(n) + A030228(n) = A000988(n) because the number of free polyominoes plus the number of polyominoes lacking bilateral symmetry equals the number of one-sided polyominoes. - Graeme McRae" (g_m(AT)mcraefamily.com), Jan 05 2006

The possible symmetry groups of a (nonempty) polyomino are the 10 subgroups of the dihedral group D_8 of order 8: D_8, 1, Z_2 (five times), Z_4, (Z_2)^2 (twice). - Benoit Jubin, Dec 30 2008

Names for first few polyominoes: "monomino", "domino", "tromino", "tetromino", "pentomino", "hexomino", "heptomino", "octomino", "enneomino", "decomino", "hendecomino", "dodecomino", ...

Barequet, Gill; Moffie, Micha; Ribo, Ares; and Rote, Guenter, Counting polyominoes on twisted cylinders. Integers 6 (2006), A22, 37 pp. (electronic).

G. Castiglione, A. Frosini, E. Munarini, A. Restivo and S. Rinaldi, Combinatorial aspects of L-convex polyominoes, to appear in European Journal of Combinatorics, 2007.

A. R. Conway and A. J. Guttmann, On two-dimensional percolation, J. Phys. A: Math. Gen. 28(1995) 891-904.

S. W. Golomb, Polyominoes, Appendix D, p. 152; Princeton Univ. Pr. NJ 1994

J. E. Goodman and J. O'Rourke, editors, Handbook of Discrete and Computational Geometry, CRC Press, 1997, p. 229.

I. Jensen, Enumerations of lattice animals and trees, arXiv cond-mat/0007239.

I. Jensen and A. J. Guttmann, Statistics of lattice animals (polyominoes) and polygons, Journal of Physics A: Mathematical and General, vol. 33, pp. L257-L263, 2000.

D. A. Klarner, The Mathematical Gardner, p. 252 Wadsworth Int. CA 1981

W. F. Lunnon, Counting polyominoes, pp. 347-372 of A. O. L. Atkin and B. J. Birch, editors, Computers in Number Theory. Academic Press, NY, 1971.

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

S. Mertens, Lattice animals: a fast enumeration algorithm and new perimeter polynomials, J. Statistical Physics, vol. 58, no. 5/6, pp. 1095-1108, Mar. 1990.

S. Mertens, Counting lattice animals: a parallel attack, Journal of Statistical Physics, vol. 66, no. 1/2, pp. 669-678, 1992.

Ed Pegg, Jr., Polyform puzzles, in Tribute to a Mathemagician, Peters, 2005, pp. 119-125.

Jaime Rangel-Mondragon, Polyominoes and Related Families, The Mathematica Journal, 9:3 (2005), 609-640.

R. C. Read, Some applications of computers in graph theory, in L. W. Beineke and R. J. Wilson, editors, Selected Topics in Graph Theory, Academic Press, NY, 1978, pp. 417-444.

D. H. Redelmeier, Counting polyominoes: yet another attack, Discrete Math., 36 (1981), 191-203.

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).

Toshihiro Shirakawa, Table of n, a(n) for n=0 ..45

K. S. Brown, Polyomino Enumerations

A. Clarke, Polyominoes

M. Keller, Counting polyforms.

Joseph Myers, Polyomino tiling

Tomas Oliveira e Silva, Animal enumerations on regular tilings in Spherical, Euclidean and Hyperbolic 2-dimensional spaces

Tomas Oliveira e Silva, Animal enumerations on the {4,4} Euclidean tiling [The enumeration to order 28]

Ed Pegg, Jr., Illustrations of polyforms

D. H. Redelmeier, Table 3 of Counting polyominoes...

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

L. Zucca, Pentominoes

L. Zucca, The 12 pentominoes

lim_{n->oo} a(n)^(1/n) = mu with 3.96 < mu < 4.64 (quoted by Castiglione et al., with a reference to Barequet et al. for the lower bound).

Sequences classifying polyominoes by symmetry group: A006746, A006747, A006748, A006749, A056877, A056878, A142886, A144553, A144554.

Cf. A001168, A033492, A000104, A054359, A054360, A001419, A000988, A030228 (chiral polyominoes).

Sequence in context: A148287 A036357 A000104 this_sequence A055192 A108555 A032203

Adjacent sequences: A000102 A000103 A000104 this_sequence A000106 A000107 A000108

nonn,hard,nice,core

N. J. A. Sloane (njas(AT)research.att.com).

Extended to n=28 by Tomas Oliveira e Silva.