A348848 Number of oriented polyominoes with 4n cells that have fourfold rotational symmetry centered at a vertex.

1, 2, 6, 19, 65, 224, 790, 2851, 10424, 38496, 143454, 538667, 2035180, 7729146, 29486904, 112942373, 434114384, 1673766428, 6471199322, 25081542410, 97431694571, 379256586232, 1479022885116

Offset

1,2

Comments

These are polyominoes of the regular tiling with Schläfli symbol {4,4}. For oriented polyominoes, chiral pairs are counted as two. This is one of the five sequences, along with A001168, needed to calculate the number of oriented polyominoes, A000988. It is the C90(n/4) sequence in the Shirakawa link. The calculation follows Redelmeier's method of inner rings.

Links

Robert A. Russell, Table of n, a(n) for n = 1..23

D. H. Redelmeier, Counting polyominoes: yet another attack, Discrete Math., 36 (1981), 191-203.

Toshihiro Shirakawa, Enumeration of Polyominoes considering the symmetry, April 2012, pp. 3-4.

Example

For a(1)=1, the polyomino is a 2 X 2 square. For a(2)=2, the two polyominoes are a chiral pair having a central 2 X 2 square with one cell attached to each edge of that square.

Crossrefs

Cf. A000988, A144553, A348849 (cell center).

Inner rings: A324406, A324407, A324408, A324409.

Sequence in context: A069728 A150083 A220065 * A047016 A307354 A307487

Adjacent sequences: A348845 A348846 A348847 * A348849 A348850 A348851

Keyword

nonn

Author

Robert A. Russell, Nov 01 2021

Status

approved