%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 90degree turns.
%C P is three numbers, according to 90degree turns of a given polyomino of n squares. Each of the three numbers corresponds to a number of 90degree 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 1square polyominoes that can turn once 90 degrees and still be considered the same phenotypic shape. a(2) would be the number of 1square polyominoes that can turn twice 90 degrees (180 degrees) and still be considered the same phenotypic shape. a(3) would be the number of 1square 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 1square polyominoes that are not radially symmetric with respect to the y and xaxes. 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
