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%I M1749 N0693 #71 Apr 15 2023 12:27:35
%S 1,1,1,2,7,18,60,196,704,2500,9189,33896,126759,476270,1802312,
%T 6849777,26152418,100203194,385221143,1485200848,5741256764,
%U 22245940545,86383382827,336093325058,1309998125640,5114451441106,19998172734786,78306011677182,307022182222506,1205243866707468,4736694001644862
%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 the 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 John Mason, <a href="/A000988/b000988.txt">Table of n, a(n) for n = 0..50</a> (terms 0..45,47,49 from Toshihiro Shirakawa).
%H W. F. Lunnon, <a href="https://doi.org/10.1093/comjnl/18.4.366">Counting multidimensional polyominoes</a>, Computer Journal 18(4) (1975), 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. [Broken link]
%H Jaime Rangel-Mondragon, <a href="https://web.archive.org/web/20151007010449/http://www.mathematica-journal.com/issue/v9i3/contents/polyominoes/polyominoes.pdf">Polyominoes and Related Families</a>, The Mathematica Journal, 9(3) (2005), 609-640. [From the internet archive]
%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 Toshihiro Shirakawa, <a href="https://www.gathering4gardner.org/g4g10gift/math/Shirakawa_Toshihiro-Harmonic_Magic_Square.pdf">Harmonic Magic Square, pp. 3-4: Enumeration of Polyominoes considering the symmetry</a>, April 2012.
%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
%F a(n) = 2*A000105(n) - A030227(n) = 2*A030228(n) + A030227(n). - _Robert A. Russell_, Feb 03 2022
%e a(0) = 1 as there is 1 empty polyomino with #cells = 0. - _Fred Lunnon_, Jun 24 2020
%Y See A006758 for another version. Subtracting 1 gives first column of A195738. Cf. A000105 (unoriented), A030228 (chiral), A030227 (achiral), A001168 (fixed).
%K nonn
%O 0,4
%A _N. J. A. Sloane_, hugh(AT)mimosa.com (D. Hugh Redelmeier)
%E a(0) = 1 added by _N. J. A. Sloane_, Jun 24 2020
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