%I A000105 M1425 N0561
%S A000105 1,1,1,2,5,12,35,108,369,1285,4655,17073,63600,238591,901971,3426576,13079255,
               50107909,
%T A000105 192622052,742624232,2870671950,11123060678,43191857688,168047007728,654999700403,
%U A000105 2557227044764,9999088822075,39153010938487,153511100594603
%N A000105 Number of polyominoes (or square animals) with n cells.
%C A000105 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
%C A000105 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
%C A000105 Names for first few polyominoes: "monomino", "domino", "tromino", "tetromino", 
               "pentomino", "hexomino", "heptomino", "octomino", "enneomino", "decomino", 
               "hendecomino", "dodecomino", ...
%D A000105 Barequet, Gill; Moffie, Micha; Ribo, Ares; and Rote, Guenter, Counting 
               polyominoes on twisted cylinders. Integers 6 (2006), A22, 37 pp. 
               (electronic).
%D A000105 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.
%D A000105 A. R. Conway and A. J. Guttmann, On two-dimensional percolation, J. Phys. 
               A: Math. Gen. 28(1995) 891-904.
%D A000105 S. W. Golomb, Polyominoes, Appendix D, p. 152; Princeton Univ. Pr. NJ 
               1994
%D A000105 J. E. Goodman and J. O'Rourke, editors, Handbook of Discrete and Computational 
               Geometry, CRC Press, 1997, p. 229.
%D A000105 I. Jensen, Enumerations of lattice animals and trees, arXiv cond-mat/
               0007239.
%D A000105 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 A000105 D. A. Klarner, The Mathematical Gardner, p. 252 Wadsworth Int. CA 1981
%D A000105 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.
%D A000105 W. F. Lunnon, Counting hexagonal and triangular polyominoes, pp. 87-100 
               of R. C. Read, editor, Graph Theory and Computing. Academic Press, 
               NY, 1972.
%D A000105 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.
%D A000105 S. Mertens, Counting lattice animals: a parallel attack, Journal of Statistical 
               Physics, vol. 66, no. 1/2, pp. 669-678, 1992.
%D A000105 Ed Pegg, Jr., Polyform puzzles, in Tribute to a Mathemagician, Peters, 
               2005, pp. 119-125.
%D A000105 Jaime Rangel-Mondragon, Polyominoes and Related Families, The Mathematica 
               Journal, 9:3 (2005), 609-640.
%D A000105 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 A000105 D. H. Redelmeier, Counting polyominoes: yet another attack, Discrete 
               Math., 36 (1981), 191-203.
%D A000105 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000105 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A000105 Toshihiro Shirakawa, <a href="b000105.txt">Table of n, a(n) for n=0 ..45</
               a>
%H A000105 K. S. Brown, <a href="http://www.mathpages.com/home/kmath039.htm">Polyomino 
               Enumerations</a>
%H A000105 A. Clarke, <a href="http://www.geocities.com/alclarke0">Polyominoes</
               a>
%H A000105 M. Keller, <a href="http://www.solitairelaboratory.com/polyenum.html">
               Counting polyforms</a>.
%H A000105 Joseph Myers, <a href="http://www.srcf.ucam.org/~jsm28/tiling/">Polyomino 
               tiling</a>
%H A000105 Tomas Oliveira e Silva, <a href="http://www.ieeta.pt/~tos/animals.html">
               Animal enumerations on regular tilings in Spherical, Euclidean and 
               Hyperbolic 2-dimensional spaces</a>
%H A000105 Tomas Oliveira e Silva, <a href="http://www.ieeta.pt/~tos/animals/a44.html">
               Animal enumerations on the {4,4} Euclidean tiling</a> [The enumeration 
               to order 28]
%H A000105 Ed Pegg, Jr., <a href="http://demonstrations.wolfram.com/PolyformExplorer/
               ">Illustrations of polyforms</a>
%H A000105 D. H. Redelmeier, <a href="a056877.png">Table 3</a> of Counting polyominoes...
%H A000105 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Polyomino.html">Link to a section of The World of Mathematics.</a>
%H A000105 L. Zucca, <a href="http://www.geocities.com/liviozuc/pag1_eng.html">Pentominoes</
               a>
%H A000105 L. Zucca, <a href="a105.gif">The 12 pentominoes</a>
%F A000105 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).
%Y A000105 Sequences classifying polyominoes by symmetry group: A006746, A006747, 
               A006748, A006749, A056877, A056878, A142886, A144553, A144554.
%Y A000105 Cf. A001168, A033492, A000104, A054359, A054360, A001419, A000988, A030228 
               (chiral polyominoes).
%Y A000105 Sequence in context: A148287 A036357 A000104 this_sequence A055192 A108555 
               A032203
%Y A000105 Adjacent sequences: A000102 A000103 A000104 this_sequence A000106 A000107 
               A000108
%K A000105 nonn,hard,nice,core
%O A000105 0,4
%A A000105 N. J. A. Sloane (njas(AT)research.att.com).
%E A000105 Extended to n=28 by Tomas Oliveira e Silva.