A202015 Number of fixed polyominoes that can produce a repeating phenotype with 1, 2, or 4 90-degree turns.

1, 1, 1, 0, 2, 2, 0, 2, 6, 1, 7, 19, 1, 7, 63, 0, 16, 216, 0, 16, 760, 3, 49, 2725, 2, 48, 9910, 0, 158, 36446

Offset

1,5

Comments

P is three numbers, according to 90-degree turns of a given polyomino of n squares. Each of the three numbers corresponds to a number of 90-degree turns (1, 2, and 4). Given P=(1), 3 numbers: a(1), a(2), and a(3) can be created. P=(1) refers to (1) squares in a polyomino. a(1) would be the number of 1-square polyominoes that can turn once 90 degrees and still be considered the same phenotypic shape. a(2) would be the number of 1-square polyominoes that can turn twice 90 degrees (180 degrees) and still be considered the same phenotypic shape. a(3) would be the number of 1-square polyominoes that can turn four times 90 degrees (360 degrees) and still be considered the same phenotypic shape. In other words, a(3) is the number of 1-square polyominoes that are not radially symmetric with respect to the y- and x-axes. Now, start over, and given P=(2), 3 numbers: a(4), a(5), and a(6) can be created.

Links

Table of n, a(n) for n=1..30.

Graeme McRae, Polyominoes

Wikipedia, Heptomino Symmetry

Example

For P=(1), a(1) = 1, a(2) = 1, and a(3) = 1.
For P=(2), a(4) = 0, a(5) = 2, and a(6) = 2.

Crossrefs

Cf. A001168 (use square animals from this list).

Sequence in context: A008281 A094671 A354826 * A193350 A021458 A279741

Adjacent sequences: A202012 A202013 A202014 * A202016 A202017 A202018

Keyword

nonn,more

Author

John Michael Feuk, Dec 08 2011

Status

approved