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We consider how many ways there are of coloring a square grid, n by 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.

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0, 0, 2, 44, 1792, 64288, 8354304, 1073447424, 549738528768, 281474691514368, 576460717407862784, 1180591619583540985856, 9671406556633359531900928 (list; graph; listen)

	OFFSET	`1,3`
	FORMULA	`a(2m+1)=2^(2m^2 + 2m - 1) - 2^(m^2 - 1)(2^(2m + 1) + 2^m) + 2^(m(m + 3)/2) a(2m)=(2^(2m^2) - 2^m^2*(2^m + 2) + 2^((m^2 + m + 2)/2))/4`
	CROSSREFS	`Cf. A054247, A054407.` `Sequence in context: A009620 A001627 A094397 this_sequence A161744 A054732 A161722` `Adjacent sequences: A140792 A140793 A140794 this_sequence A140796 A140797 A140798`
	KEYWORD	`nonn`
	AUTHOR	`Anthony C Robin (anthony_robin(AT)hotmail.com), Jul 15 2008`

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.

AT&T Labs Research