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, 140221383170146560, 203716633441803914880, 16384, 201014784, 1838265306048, 12526017160372992

Offset

1,1

Comments

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

Links

Jason Davies, Table of n, a(n) for n = 1..34

Jason 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, A391612.

Sequence in context: A333438 A232840 A113905 * A379764 A099202 A139288

Adjacent sequences: A200042 A200043 A200044 * A200046 A200047 A200048

Keyword

nonn,tabl

Author

Jason Davies, Nov 14 2011

Extensions

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

T(6,5) corrected by Jason Davies, Dec 11 2025

T(6,6) to T(7,4) from Jason Davies, Dec 14 2025

T(7,5) to T(7,6) from Jason Davies, Dec 21 2025

Status

approved