%I #6 Aug 12 2016 06:55:34

%S 1,1,0,1,0,1,1,0,1,2,1,0,5,13,9,1,0,11,102,331,44,1,0,24,1233,31550,

%T 17651,265,1,0,77,17773,4320344,19336609,1386377,1854,1,0,222,295717,

%U 697988671,29135818243,21048933326,148410280,14833,1,0,700,5288444

%N T(n,k)=Number of nXk arrays containing k copies of 0..n-1 with no element 1 greater than its north, west or southwest neighbor modulo n and the upper left element equal to 0.

%C Table starts

%C ......1...........1..............1...............1..............1............1

%C ......0...........0..............0...............0..............0............0

%C ......1...........1..............5..............11.............24...........77

%C ......2..........13............102............1233..........17773.......295717

%C ......9.........331..........31550.........4320344......697988671.118566001021

%C .....44.......17651.......19336609.....29135818243.51215246659276

%C ....265.....1386377....21048933326.456207481947741

%C ...1854...148410280.36737059793206

%C ..14833.20588092054

%C .133496

%H R. H. Hardin, <a href="/A266904/b266904.txt">Table of n, a(n) for n = 1..60</a>

%e Some solutions for n=4 k=4

%e ..0..0..3..2....0..2..2..1....0..2..1..3....0..2..1..3....0..2..0..2

%e ..2..0..2..0....0..0..2..1....3..1..3..1....2..1..3..1....2..0..3..2

%e ..1..3..1..3....0..3..1..3....2..0..3..1....1..3..2..0....1..3..3..1

%e ..3..2..1..1....3..1..3..2....2..0..2..0....0..2..0..3....1..3..1..0

%Y Column 1 is A000166(n-1).

%K nonn,tabl

%O 1,10

%A _R. H. Hardin_, Jan 05 2016