A056878 - OEIS

A056878

Number of polyominoes with n cells, symmetric about diagonal 2.

0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 2, 3, 3, 5, 6, 14, 9, 20, 20, 56, 32, 80, 64, 224, 114, 315, 217, 863, 397, 1234, 751, 3331, 1400, 4816, 2632, 12815, 4973, 18792, 9349, 49400, 17810, 73338, 33557, 190643, 64309, 286368, 121511, 737532, 233891, 1119215, 443271, 2859154

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OFFSET

1,11

COMMENTS

The sequence refers to those polyominoes having reflective symmetry on both diagonals, consequent 180-degree rotational symmetry, but without 90-degree rotational symmetry. Such polyominoes with rotational symmetry symmetry centered about square centers and vertices are enumerated by A351159 and A351160 respectively. - John Mason, Feb 17 2022

LINKS

Robert A. Russell, Table of n, a(n) for n = 1..87

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

a(n) = A351159(n) + A351160(n/2) for even n, otherwise a(n) = A351159(n). - John Mason, Feb 17 2022

EXAMPLE

For a(7)=1, the heptomino with exactly fourfold symmetry and axes of symmetry parallel to the diagonals of the cells is composed of two 2 X 2 squares with one cell in common. For a(8)=1, the octomino is composed of a 2 X 2 square and the four cells adjacent to two nonadjacent cells of that square.

CROSSREFS

Cf. A000105, A001168, A006746, A056877, A006748, A056878, A006747, A006749.

Sequences classifying polyominoes by symmetry group: A000105, A006746, A006747, A006748, A006749, A056877, A056878, A142886, A144553, A144554, A351159, A351160.

Sequence in context: A121400 A238003 A218932 * A270520 A092557 A333295

Adjacent sequences: A056875 A056876 A056877 * A056879 A056880 A056881

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Sep 03 2000

EXTENSIONS

More terms from Robert A. Russell, Jan 18 2019

STATUS

approved