

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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


LINKS

Table of n, a(n) for n=1..16.


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*m1)2^(m^21)*(2^(2*m+1)+2^m)+2^(m*(m+3)/2)])); s \\ Colin Barker, Mar 28 2014


CROSSREFS

Cf. A054247, A054407.
Sequence in context: A202747 A094397 A213067 * A161744 A208045 A267070
Adjacent sequences: A140792 A140793 A140794 * A140796 A140797 A140798


KEYWORD

nonn


AUTHOR

Anthony C Robin, Jul 15 2008


EXTENSIONS

More terms from Colin Barker, Mar 28 2014


STATUS

approved



