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A343562
The number of n-cell polyominoes with a line of symmetry parallel to the edges.
1
1, 1, 1, 3, 4, 8, 12, 28, 44, 98, 157, 359, 583, 1324, 2183, 4961, 8263, 18729, 31477, 71231, 120605, 272380, 464188, 1046516, 1793505, 4036645, 6952368, 15623258, 27026985, 60645746, 105327495, 236021747, 411377265, 920654994, 1609862767, 3598552287
OFFSET
1,4
COMMENTS
The polyominoes counted here may have additional symmetries (mirror axes along diagonals or rotational symmetries or two orthogonal mirror axes...). The mirror axes may run through cell edges or through cell centers.
LINKS
FORMULA
a(n) = A056877(n) + A142886(n) + A006746(n).
EXAMPLE
For n=4 the 3 polyominoes are (i) the 2x2 block, (ii) the straight 1x4 block and (iii) the T.
CROSSREFS
KEYWORD
nonn,hard
AUTHOR
R. J. Mathar, Sep 29 2021
EXTENSIONS
More terms from John Mason, Dec 16 2021
STATUS
approved