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A000988 Number of one-sided polyominoes with n cells.
(Formerly M1749 N0693)
16
1, 1, 2, 7, 18, 60, 196, 704, 2500, 9189, 33896, 126759, 476270, 1802312, 6849777, 26152418, 100203194, 385221143, 1485200848, 5741256764, 22245940545, 86383382827, 336093325058, 1309998125640, 5114451441106, 19998172734786, 78306011677182, 307022182222506, 1205243866707468, 4736694001644862 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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, Jan 05 2006

Names for first few polyominoes: monomino, domino, tromino, tetromino, pentomino, hexomino, heptomino, octomino, enneomino, decomino, hendecomino, dodecomino, ...

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.

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).

LINKS

Toshihiro Shirakawa, Table of n, a(n) for n=0 ..45

Ed Pegg, Jr., Illustrations of polyforms

D. H. Redelmeier, Counting polyominoes: yet another attack, Discrete Math., 36 (1981), 191-203.

Eric Weisstein's World of Mathematics, Polyomino

CROSSREFS

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

Sequence in context: A046866 A214836 A176813 * A185308 A002214 A218684

Adjacent sequences:  A000985 A000986 A000987 * A000989 A000990 A000991

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, hugh(AT)mimosa.com (D. Hugh Redelmeier)

STATUS

approved

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Last modified September 16 15:27 EDT 2014. Contains 246817 sequences.