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T(n,k)=Number of nXk arrays containing k copies of 0..n-1 with no element 1 greater than its north, southwest or southeast neighbor modulo n and the upper left element equal to 0.
6

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

%S 1,1,0,1,0,1,1,0,4,2,1,0,8,23,9,1,0,22,376,398,44,1,0,54,7137,40298,

%T 23432,265,1,0,142,147378,5336960,25499147,1841274,1854,1,0,368,

%U 3267167,807737754,39048984268,28504890050,193070360,14833,1,0,974,75854154

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

%C Table starts

%C .....1.........1...........1...........1.........1............1........1...1.1

%C .....0.........0...........0...........0.........0............0........0...0.0

%C .....1.........4...........8..........22........54..........142......368.974

%C .....2........23.........376........7137....147378......3267167.75854154

%C .....9.......398.......40298.....5336960.807737754.133402295812

%C ....44.....23432....25499147.39048984268

%C ...265...1841274.28504890050

%C ..1854.193070360

%C .14833

%H R. H. Hardin, <a href="/A266921/b266921.txt">Table of n, a(n) for n = 1..50</a>

%e Some solutions for n=4 k=4

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

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

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

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

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

%K nonn,tabl

%O 1,9

%A _R. H. Hardin_, Jan 06 2016