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A140795
We consider how many ways there are of coloring a square grid, n X n, using just two colors, black & white say. If the resulting grid has rotational symmetry of order two only, then the number of different grids is given by this sequence. None of these counted are the images of any of the others under a reflection or a rotation of 90 degrees. If one wishes to count these as different, then each of these numbers can be multiplied by 4.
0
0, 0, 2, 44, 1792, 64288, 8354304, 1073447424, 549738528768, 281474691514368, 576460717407862784, 1180591619583540985856, 9671406556633359531900928, 79228162514246041720191975424, 2596148429267404554864448650608640, 85070591730234614676028659138035712000
OFFSET
1,3
FORMULA
a(2m+1) = 2^(2*m^2 + 2*m - 1) - 2^(m^2 - 1)*(2^(2*m + 1) + 2^m) + 2^(m*(m + 3)/2).
a(2m) = (2^(2*m^2) - 2^m^2*(2^m + 2) + 2^((m^2 + m + 2)/2))/4.
PROG
(PARI) s=[0]; for(m=1, 15, s=concat(s, [(2^(2*m^2)-2^m^2*(2^m+2)+2^((m^2+m+2)/2))/4, 2^(2*m^2+2*m-1)-2^(m^2-1)*(2^(2*m+1)+2^m)+2^(m*(m+3)/2)])); s \\ Colin Barker, Mar 28 2014
CROSSREFS
Sequence in context: A202747 A094397 A213067 * A161744 A208045 A267070
KEYWORD
nonn
AUTHOR
Anthony C Robin, Jul 15 2008
EXTENSIONS
More terms from Colin Barker, Mar 28 2014
STATUS
approved