A144554 Number of polyominoes with n cells whose symmetry group (excluding reflections) has order at least 2.

1, 1, 1, 3, 3, 7, 8, 25, 25, 82, 85, 302, 307, 1111, 1131, 4216, 4267, 16076, 16253, 61976, 62475, 239927, 241447, 933576, 937574, 3644073, 3653624, 14267757, 14281711, 55996279, 55968648, 220244340, 219829297, 867868410, 865120447, 3425522409, 3410557920, 13540713898, 13466370893, 53596553368

Offset: 1

Author

Fred Schneider, Dec 28 2008

Keywords

• nonn

Comments

In other words, a(n) is the number of polyominoes with n cells having at least 180-degree rotational symmetry. - John Mason, Feb 14 2022

Links

• John Mason, Table of n, a(n) for n = 1..50
• Tomás Oliveira e Silva, Enumeration of polyominoes
• D. H. Redelmeier, Counting polyominoes: yet another attack, Discrete Math., 36 (1981), 191-203.
• D. H. Redelmeier, Table 3 of Counting polyominoes...

Crossrefs

Sequences classifying polyominoes by symmetry group: A000105, A006746, A006747, A006748, A006749, A056877, A056878, A142886, A144553, A144554.

Programs

Mathematica

A000105 = Cases[Import["https://oeis.org/A000105/b000105.txt", "Table"], {, }][[All, 2]];
A006749 = Cases[Import["https://oeis.org/A006749/b006749.txt", "Table"], {, }][[All, 2]];
A006746 = Cases[Import["https://oeis.org/A006746/b006746.txt", "Table"], {, }][[All, 2]];
A006748 = Cases[Import["https://oeis.org/A006748/b006748.txt", "Table"], {, }][[All, 2]];
a[n_] := A000105[[n+1]] - A006749[[n]] - A006746[[n]] - A006748[[n]];
Table[a[n], {n, 1, 48}] (* Jean-François Alcover, Aug 17 2022 *)

Formula

This is the sum of A142886, A056877, A144553, A056878 and A006747. - Joseph Myers, Dec 31 2008

a(n) = A000105(n) - A006749(n) - A006746(n) - A006748(n). - John Mason, Feb 14 2022

Extensions

Edited by N. J. A. Sloane, Jan 01 2009

17 additional terms (just summing the terms from the 5 sequences specified in the description) Fred Schneider, Jan 03 2009

a(28) from John Mason, Oct 05 2021

a(29)-a(36) from John Mason, Oct 16 2021

Terms a(37) and beyond from John Mason, Feb 14 2022