A179618 T(n,k) = Half the number of (n+1) X (k+1) 0..2 arrays with every 2 X 2 subblock diagonal sum differing from its antidiagonal sum by more than 2.

5, 11, 11, 21, 35, 21, 43, 93, 93, 43, 85, 269, 314, 269, 85, 171, 747, 1213, 1213, 747, 171, 341, 2115, 4375, 6427, 4375, 2115, 341, 683, 5933, 16334, 31387, 31387, 16334, 5933, 683, 1365, 16717, 59925, 159651, 202841, 159651, 59925, 16717, 1365, 2731

Offset

1,1

Comments

T(n,k) apparently is also the number of ways to tile an (n+2) X (k+2) rectangle with 1 X 1 and 2 X 2 tiles.

Links

R. H. Hardin, Table of n, a(n) for n = 1..839

Example

Table starts
     5     11      21        43         85         171           341
    11     35      93       269        747        2115          5933
    21     93     314      1213       4375       16334         59925
    43    269    1213      6427      31387      159651        795611
    85    747    4375     31387     202841     1382259       9167119
   171   2115   16334    159651    1382259    12727570     113555791
   341   5933   59925    795611    9167119   113555791    1355115601
   683  16717  221799   4005785   61643709  1029574631   16484061769
  1365  47003  817280  20064827  411595537  9258357134  198549329897
  2731 132291 3018301 100764343 2758179839 83605623809 2403674442213
Some solutions for 6 X 6:
  0 2 0 2 0 2    0 1 0 2 1 2    0 2 0 2 0 2    0 1 0 2 0 1
  2 0 2 0 2 1    2 0 2 0 2 0    2 0 1 0 1 0    2 0 2 0 2 0
  0 2 0 2 0 2    1 2 1 2 0 2    0 2 0 2 0 2    0 2 0 2 0 2
  2 0 2 0 2 1    2 0 2 0 1 0    1 0 2 0 2 0    1 0 2 0 2 0
  0 2 0 2 0 2    0 2 0 2 0 2    0 2 0 2 0 2    0 2 1 2 1 2
  1 0 1 0 1 0    2 1 2 1 2 0    2 1 2 1 2 1    2 0 2 0 2 0

Crossrefs

Diagonal is A063443(n+2).

Column 1 is A001045(n+3).

Column 2 is A054854(n+2).

Column 3 is A054855(n+2).

Column 4 is A063650(n+2).

Column 5 is A063651(n+2).

Column 6 is A063652(n+2).

Column 7 is A063653(n+2).

Column 8 is A063654(n+2).

Sequence in context: A060846 A352354 A113002 * A058197 A289464 A289580

Adjacent sequences: A179615 A179616 A179617 * A179619 A179620 A179621

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 10 2011

Status

approved