A343562 The number of n-cell polyominoes with a line of symmetry parallel to the edges.

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

Author

R. J. Mathar, Sep 29 2021

Keywords

• nonn
• hard

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.

Examples

			For n=4 the 3 polyominoes are (i) the 2x2 block, (ii) the straight 1x4 block and (iii) the T.
		

Links

• John Mason, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A056877, A142886, A006746.

Formula

a(n) = A056877(n) + A142886(n) + A006746(n).

Extensions

More terms from John Mason, Dec 16 2021