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

1,4

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

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

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

Cf. A056877, A142886, A006746.

Sequence in context: A329730 A153339 A275989 * A033955 A327466 A049720

Adjacent sequences: A343559 A343560 A343561 * A343563 A343564 A343565

Keyword

nonn,hard

Author

R. J. Mathar, Sep 29 2021

Extensions

More terms from John Mason, Dec 16 2021

Status

approved