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A000988 Number of one-sided polyominoes with n cells.
(Formerly M1749 N0693)

%I M1749 N0693

%S 1,1,2,7,18,60,196,704,2500,9189,33896,126759,476270,1802312,6849777,

%T 26152418,100203194,385221143,1485200848,5741256764,22245940545,

%U 86383382827,336093325058,1309998125640,5114451441106,19998172734786,78306011677182,307022182222506,1205243866707468,4736694001644862

%N Number of one-sided polyominoes with n cells.

%C A000105(n) + A030228(n) = a(n) because the number of free polyominoes plus the number of polyominoes lacking bilateral symmetry equals the number of one-sided polyominoes. - _Graeme McRae_, Jan 05 2006

%C Names for first few polyominoes: monomino, domino, tromino, tetromino, pentomino, hexomino, heptomino, octomino, enneomino (aka nonomino), decomino, hendecomino (aka undecomino), dodecomino, ...

%D S. W. Golomb, Polyominoes. Scribner's, NY, 1965; second edition (Polyominoes: Puzzles, Packings, Problems and Patterns) Princeton Univ. Press, 1994.

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

%D W. F. Lunnon, personal communication.

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

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

%H Toshihiro Shirakawa, <a href="/A000988/b000988.txt">Table of n, a(n) for n=1 ..45</a>

%H W. F. Lunnon, <a href="https://doi.org/10.1093/comjnl/18.4.366">Counting multidimensional polyominoes</a>, Computer Journal 18 (1975), no. 4, pp. 366-367.

%H Ed Pegg, Jr., <a href="http://demonstrations.wolfram.com/PolyformExplorer/">Illustrations of polyforms</a>

%H Jaime Rangel-Mondragon, <a href="http://www.mathematica-journal.com/issue/v9i3/polyominoes.html">Polyominoes and Related Families</a>, The Mathematica Journal, 9:3 (2005), 609-640.

%H D. H. Redelmeier, <a href="http://dx.doi.org/10.1016/0012-365X(81)90237-5">Counting polyominoes: yet another attack</a>, Discrete Math., 36 (1981), 191-203.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Polyomino.html">Polyomino</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Polyomino">Polyomino</a>

%F a(n) = 2*A006749(n) + A006746(n) + A006748(n) + 2*A006747(n) + A056877(n) + A056878(n) + 2*A144553(n) + A142886(n). - _Andrew Howroyd_, Dec 04 2018

%Y See A006758 for another version. Subtracting 1 gives first column of A195738. See also A030228 (chiral polyominoes), A000105.

%K nonn

%O 1,3

%A _N. J. A. Sloane_, hugh(AT)mimosa.com (D. Hugh Redelmeier)

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Last modified February 21 01:29 EST 2019. Contains 320364 sequences. (Running on oeis4.)