A006748 Number of diagonally symmetric polyominoes with n cells.

0, 0, 1, 0, 2, 2, 7, 5, 26, 22, 91, 79, 326, 301, 1186, 1117, 4352, 4212, 16119, 15849, 60174, 60089, 226146, 228426, 854803, 872404, 3247207, 3342579, 12389106, 12850662, 47448984, 49544820, 182338754, 191529007, 702807040, 742163178, 2716205709, 2882119756

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

This sequence counts polyominoes with exactly the symmetry group of order 2 generated by a single reflection about a diagonal.

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• John Mason, Table of n, a(n) for n = 1..50 (terms up to a(47) from Robert A. Russell)
• 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...
• Toshihiro Shirakawa, Harmonic Magic Square, pp 3-4: Enumeration of Polyominoes considering the symmetry, April 2012.

Crossrefs

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

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

Formula

a(n) = (A346800(n) - A142886(n)) / 2 - A056878(n). - Robert A. Russell, Aug 25 2021

Extensions

Extended to n=28 by Tomás Oliveira e Silva