A255256 Number A(n,k) of 2-colorings of a k X n rectangle such that no nontrivial subsquare has monochromatic corners; square array A(n,k), n>=0, k>=0, read by antidiagonals.
1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 8, 14, 8, 1, 1, 16, 50, 50, 16, 1, 1, 32, 178, 276, 178, 32, 1, 1, 64, 634, 1498, 1498, 634, 64, 1, 1, 128, 2258, 8352, 10980, 8352, 2258, 128, 1, 1, 256, 8042, 46730, 85138, 85138, 46730, 8042, 256, 1, 1, 512, 28642, 260204, 655090, 781712, 655090, 260204, 28642, 512, 1
Offset: 0
Examples
A(2,2) = 2^(2*2) - 2 = 14 because there are exactly two of sixteen 2-colorings of the 2 X 2 square resulting in nontrivial subsquares with monochromatic corners. Square array A(n,k) begins: 1, 1, 1, 1, 1, 1, 1, ... 1, 2, 4, 8, 16, 32, 64, ... 1, 4, 14, 50, 178, 634, 2258, ... 1, 8, 50, 276, 1498, 8352, 46730, ... 1, 16, 178, 1498, 10980, 85138, 655090, ... 1, 32, 634, 8352, 85138, 781712, 6965108, ... 1, 64, 2258, 46730, 655090, 6965108, 58339148, ...
Links
- Alois P. Heinz, Antidiagonals n = 0..12