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A030227 Number of achiral polyominoes with n cells. 3
1, 1, 2, 3, 6, 10, 20, 34, 70, 121, 250, 441, 912, 1630, 3375, 6092, 12624, 22961, 47616, 87136, 180811, 332549, 690398, 1275166, 2648422, 4909364, 10199792, 18966700, 39416488, 73497642, 152777230, 285569898, 593717419, 1112188817, 2312672439, 4340728280 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Polyominoes with n cells and at least one line of reflection symmetry. - Joshua Zucker, Mar 08 2008

LINKS

Robert A. Russell, 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) = A000105(n) - A030228(n) = 2*A000105(n) - A000988(n). - Andrew Howroyd, Dec 04 2018

a(n) = A006746(n) + A006748(n) + A056877(n) + A056878(n) + A142886(n) = A000988(n) - 2*A030228(n). - Robert A. Russell, Feb 02 2019

EXAMPLE

For a(4)=3, the achiral tetrominoes are a 2 X 2 square, a 1 X 4 rectangle, and a cell plus three cells adjacent to it (forming a shortened T).

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_] := 2*A000105[[n + 1]] - A000988[[n]];

Array[a, 45] (* Jean-François Alcover, Sep 08 2019, after Andrew Howroyd *)

CROSSREFS

Cf. A000988 (oriented), A000105 (unoriented), A030228 (chiral).

Cf. A006746, A006748, A056877, A056878, A142886 (subcategories).

Sequence in context: A135452 A077027 A030436 * A180272 A319436 A061551

Adjacent sequences:  A030224 A030225 A030226 * A030228 A030229 A030230

KEYWORD

nonn

AUTHOR

David W. Wilson

EXTENSIONS

a(23)-a(36) 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 10:15 EDT 2019. Contains 328026 sequences. (Running on oeis4.)