A200045 Number T(n,m) of ways of 4-coloring an n X m grid so that there is no rectangle with all 4 corners the same color.

4, 16, 252, 64, 3912, 228984, 256, 59928, 12870096, 2545607472, 1024, 906912, 696448224, 465659203104, 272454472598400, 4096, 13571712, 36376835616, 79102304162784, 140221913588582784

Offset

1,1

Comments

The rectangles have sides parallel to the x- and y-axes.

Links

Table of n, a(n) for n=1..20.

J. D. Davies, Number of unique rectangle-free 4-colourings for an nxm grid

Example

Triangle starts:
     4;
    16,    252;
    64,   3912,    228984;
   256,  59928,  12870096,   2545607472;
  1024, 906912, 696448224, 465659203104, 272454472598400;
  ...

Crossrefs

Cf. A252778, A252780, A252839.

Sequence in context: A333438 A232840 A113905 * A099202 A139288 A152921

Adjacent sequences: A200042 A200043 A200044 * A200046 A200047 A200048

Keyword

nonn,tabl,more

Author

Jason Davies, Nov 14 2011

Extensions

T(6,5) from Jason Davies, Nov 08 2012

Status

approved