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

0,5

Links

Alois P. Heinz, Antidiagonals n = 0..12

Example

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, ...

Crossrefs

Columns (or rows) k=0-5 give: A000012, A000079, A055099, A133357, A255255, A255262.

Main diagonal gives A018803.

Sequence in context: A256894 A364856 A099594 * A328887 A299906 A117401

Adjacent sequences: A255253 A255254 A255255 * A255257 A255258 A255259

Keyword

nonn,tabl

Author

Alois P. Heinz, Feb 19 2015

Status

approved