John Michael Feuk - cp's OEIS frontend

User: John Michael Feuk

John Michael Feuk has authored 1 sequences.

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

John Michael Feuk, Dec 08 2011

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.

			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.

Graeme McRae, Polyominoes
Wikipedia, Heptomino Symmetry

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

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User: John Michael Feuk

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

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