A140789 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 TWO lines of symmetry, 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 rotation. If one wishes to count these as different, then each of these numbers can be multiplied by 2.

0, 1, 8, 32, 448, 2240, 64512, 556032, 33521664, 553615360, 68717379584, 2233380896768, 562949684985856, 36310271727239168, 18446744004990074880, 2370406613402957905920, 2417851639194073977323520, 620178945462269582252179456, 1267650600228193372699684241408

Offset

1,3

Links

Table of n, a(n) for n=1..19.

Formula

a(2m) = 2^(m^2 - 1)*(2^m + 1) - 2^(m*(m + 1)/2).

a(2m+1)= 2^(m^2 + 2*m + 1) - 2^((m^2 + 3*m + 2)/2).

Prog

(PARI) s=[0]; for(m=1, 15, s=concat(s, [2^(m^2-1)*(2^m+1)-2^(m*(m+1)/2), 2^(m^2+2*m+1)-2^((m^2+3*m+2)/2)])); s \\ Colin Barker, Mar 28 2014

Crossrefs

Cf. A140650.

Sequence in context: A034193 A159277 A214539 * A120781 A288454 A139286

Adjacent sequences: A140786 A140787 A140788 * A140790 A140791 A140792

Keyword

nonn

Author

Anthony C Robin, Jul 14 2008

Extensions

More terms from Colin Barker, Mar 28 2014

Status

approved