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A056877 Number of polyominoes with n cells, symmetric about axis 2. 20
0, 1, 1, 1, 1, 2, 3, 4, 4, 8, 10, 15, 17, 30, 35, 60, 64, 117, 128, 236, 241, 459, 476, 937, 912, 1813, 1789, 3706, 3456, 7187, 6779, 14712, 13161, 28571, 25839, 58457, 50348, 113798, 98957, 232718, 193375, 453969, 380522, 927601, 745248, 1813219, 1468202, 3702063 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

This sequence counts polyominoes with exactly the symmetry group D_2 generated by horizontal and vertical reflections.

LINKS

Robert A. Russell, Table of n, a(n) for n = 1..81

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...

Wikipedia, Symmetries of polyominoes

EXAMPLE

For a(8)=4, the four octominoes with exactly fourfold symmetry and axes of symmetry parallel to the edges of the cells are a row of eight cells, two adjacent rows of four cells, a row of four cells with another four cells adjacent to its center cells, and a row of four cells with another four cells adjacent to its end cells (but not in the original row).

CROSSREFS

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

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

Sequence in context: A224038 A241037 A097093 * A267232 A269606 A269640

Adjacent sequences:  A056874 A056875 A056876 * A056878 A056879 A056880

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Sep 03 2000

EXTENSIONS

More terms from Robert A. Russell, Jan 16 2019

STATUS

approved

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Last modified October 22 04:25 EDT 2019. Contains 328315 sequences. (Running on oeis4.)