A144554 - OEIS

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

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OFFSET

1,4

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...

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

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 *)

CROSSREFS

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

Sequence in context: A056357 A288728 A213942 * A177936 A337975 A143088

Adjacent sequences: A144551 A144552 A144553 * A144555 A144556 A144557

KEYWORD

nonn

AUTHOR

Fred Schneider, Dec 28 2008

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

STATUS

approved