This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A140795 #8 Mar 29 2014 03:07:57 %S A140795 0,0,2,44,1792,64288,8354304,1073447424,549738528768,281474691514368, %T A140795 576460717407862784,1180591619583540985856,9671406556633359531900928, %U A140795 79228162514246041720191975424,2596148429267404554864448650608640,85070591730234614676028659138035712000 %N 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. %F A140795 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). %F A140795 a(2m) = (2^(2*m^2) - 2^m^2*(2^m + 2) + 2^((m^2 + m + 2)/2))/4. %o A140795 (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 %Y A140795 Cf. A054247, A054407. %K A140795 nonn %O A140795 1,3 %A A140795 _Anthony C Robin_, Jul 15 2008 %E A140795 More terms from _Colin Barker_, Mar 28 2014