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A202015 Number of fixed polyominoes that can produce a repeating phenotype with 1, 2, or 4 90-degree turns. 0

%I

%S 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,

%T 9910,0,158,36446

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

%C 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.

%H Graeme McRae, <a href="http://2000clicks.com/mathhelp/CountingPolyominoes.aspx">Polyominoes</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Heptomino">Heptomino Symmetry</a>

%e For P=(1), a(1) = 1, a(2) = 1, and a(3) = 1.

%e For P=(2), a(4) = 0, a(5) = 2, and a(6) = 2.

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

%K nonn,more

%O 1,5

%A _John Michael Feuk_, Dec 08 2011

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Last modified January 24 10:01 EST 2022. Contains 350534 sequences. (Running on oeis4.)