OFFSET
0,4
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 the first few polyominoes: monomino, domino, tromino, tetromino, pentomino, hexomino, heptomino, octomino, enneomino (aka nonomino), decomino, hendecomino (aka undecomino), 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.
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
John Mason, Table of n, a(n) for n = 0..50 (terms 0..45,47,49 from Toshihiro Shirakawa).
W. F. Lunnon, Counting multidimensional polyominoes, Computer Journal 18(4) (1975), 366-367.
Ed Pegg, Jr., Illustrations of polyforms.
Jaime Rangel-Mondragon, Polyominoes and Related Families, The Mathematica Journal, 9(3) (2005), 609-640. [Broken link]
Jaime Rangel-Mondragon, Polyominoes and Related Families, The Mathematica Journal, 9(3) (2005), 609-640. [From the internet archive]
D. H. Redelmeier, Counting polyominoes: yet another attack, Discrete Math., 36 (1981), 191-203.
Toshihiro Shirakawa, Harmonic Magic Square, pp. 3-4: Enumeration of Polyominoes considering the symmetry, April 2012.
Eric Weisstein's World of Mathematics, Polyomino.
Wikipedia, Polyomino.
FORMULA
EXAMPLE
a(0) = 1 as there is 1 empty polyomino with #cells = 0. - Fred Lunnon, Jun 24 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, hugh(AT)mimosa.com (D. Hugh Redelmeier)
EXTENSIONS
a(0) = 1 added by N. J. A. Sloane, Jun 24 2020
STATUS
approved