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A000988
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Number of one-sided polyominoes with n cells.
(Formerly M1749 N0693)
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10
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1, 1, 2, 7, 18, 60, 196, 704, 2500, 9189, 33896, 126759, 476270, 1802312, 6849777, 26152418, 100203194, 385221143, 1485200848, 5741256764, 22245940545, 86383382827, 336093325058, 1309998125640
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| 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" (g_m(AT)mcraefamily.com), Jan 05 2006
Names for first few polyominoes: "monomino", "domino", "tromino", "tetromino", "pentomino", "hexomino", "heptomino", "octomino", "enneomino", "decomino", "hendecomino", "dodecomino", ...
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REFERENCES
| S. W. Golomb, Polyominoes. Scribner's, NY, 1965; second edition ( Polyominoes: Puzzles, Packings, Problems and Patterns) Princeton Univ. Press, 1994.
J. E. Goodman and J. O'Rourke, editors, Handbook of Discrete and Computational Geometry, CRC Press, 1997, p. 229.
W. F. Lunnon, personal communication.
W. F. Lunnon, Counting multidimensional polyominoes. Computer Journal 18 (1975), no. 4, pp. 366-367.
Jaime Rangel-Mondragon, Polyominoes and Related Families, The Mathematica Journal, 9:3 (2005), 609-640.
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).
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LINKS
| Toshihiro Shirakawa, Table of n, a(n) for n=0 ..45
Ed Pegg, Jr., Illustrations of polyforms
Eric Weisstein's World of Mathematics, Polyomino
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CROSSREFS
| See A006758 for another version. Subtracting 1 gives first column of A195738. See also A030228 (chiral polyominoes), A000105.
Sequence in context: A046672 A046866 A176813 * A002214 A100408 A103034
Adjacent sequences: A000985 A000986 A000987 * A000989 A000990 A000991
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), hugh(AT)mimosa.com (D. Hugh Redelmeier)
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