A006748 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A006748

Number of diagonally symmetric polyominoes with n cells.
(Formerly M0366)

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,5

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.

FORMULA

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

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.

Sequence in context: A223000 A058625 A300126 * A193548 A131049 A142070

Adjacent sequences: A006745 A006746 A006747 * A006749 A006750 A006751

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

Extended to n=28 by Tomás Oliveira e Silva

STATUS

approved