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

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, Jan. 1992.

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

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.

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]

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).

Cf. A001168, A006749, A033492, A000104, A054359, A054360, A001419, A000988, A030228 (chiral polyominoes).

Sequence in context: A054359 A036357 A000104 this_sequence A055192 A108555 A032203

Adjacent sequences: A000102 A000103 A000104 this_sequence A000106 A000107 A000108

nonn,hard,nice,core

njas

Extended to n=28 by Tomas Oliveira e Silva.