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A202015 Number of fixed polyominoes that can produce a repeating phenotype with 1, 2, or 4 90-degree turns. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A278483 A008281 A094671 * A193350 A021458 A279741

Adjacent sequences:  A202012 A202013 A202014 * A202016 A202017 A202018

KEYWORD

nonn,more

AUTHOR

John Michael Feuk, Dec 08 2011

STATUS

approved

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Last modified November 27 06:49 EST 2021. Contains 349365 sequences. (Running on oeis4.)