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A030228 Number of chiral polyominoes with n cells. 6
0, 0, 0, 2, 6, 25, 88, 335, 1215, 4534, 16823, 63159, 237679, 900341, 3423201, 13073163, 50095285, 192599091, 742576616, 2870584814, 11122879867, 43191525139, 168046317330, 654998425237, 2557224396342, 9999083912711, 39153000738695, 153511081627903 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

A000105(n) + a(n) = A000988(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

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..45

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

FORMULA

a(n) = A000988(n) - A000105(n). - Graeme McRae, Jan 05 2006

a(n) = A006749(n) + A006747(n) + A144553(n). - Andrew Howroyd, Dec 04 2018

a(n) = A000105(n) - A030227(n) = (A000988(n) - A030227(n)) / 2. - Robert A. Russell, Feb 02 2019

EXAMPLE

For a(4)=2, the two chiral tetrominoes are XXX and XX .

                                           X        XX

MATHEMATICA

A000105 = Cases[Import["https://oeis.org/A000105/b000105.txt", "Table"], {_, _}][[All, 2]];

A000988 = Cases[Import["https://oeis.org/A000988/b000988.txt", "Table"], {_, _}][[All, 2]];

a[n_] := A000988[[n]] - A000105[[n + 1]];

Array[a, 45] (* Jean-Fran├žois Alcover, Sep 08 2019, after Graeme McRae *)

CROSSREFS

Cf. A000988 (oriented), A000105 (unoriented), A030227 (achiral).

Cf. A006747, A006749, A144553 (subcategories).

Sequence in context: A073545 A103063 A220191 * A066317 A027104 A019048

Adjacent sequences:  A030225 A030226 A030227 * A030229 A030230 A030231

KEYWORD

nonn

AUTHOR

David W. Wilson

EXTENSIONS

Terms a(23) and beyond from Andrew Howroyd, Dec 04 2018

Name edited by Robert A. Russell, Feb 03 2019

STATUS

approved

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Last modified October 15 00:14 EDT 2019. Contains 328025 sequences. (Running on oeis4.)