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%I #5 Aug 12 2016 06:55:34
%S 1,1,0,1,0,1,1,0,1,2,1,0,2,11,9,1,0,5,95,314,44,1,0,18,1267,27315,
%T 16904,265,1,0,64,19605,3343156,18101569,1344296,1854,1,0,200,322100,
%U 501954949,27013215515,20154412479,145081212,14833,1,0,608,5798969,84214451308
%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 northwest neighbor modulo n and the upper left element equal to 0.
%C Table starts
%C .....1.........1...........1...........1.........1...........1.......1...1.1.1
%C .....0.........0...........0...........0.........0...........0.......0...0.0
%C .....1.........1...........2...........5........18..........64.....200.608
%C .....2........11..........95........1267.....19605......322100.5798969
%C .....9.......314.......27315.....3343156.501954949.84214451308
%C ....44.....16904....18101569.27013215515
%C ...265...1344296.20154412479
%C ..1854.145081212
%C .14833
%e Some solutions for n=4 k=4
%e ..0..3..3..3....0..3..1..0....0..0..0..2....0..3..3..2....0..0..3..1
%e ..0..2..2..1....3..3..1..0....0..3..2..2....0..3..3..2....0..2..2..1
%e ..2..2..1..1....2..2..1..0....3..3..1..1....2..2..1..1....3..2..1..1
%e ..1..0..0..3....2..2..1..3....3..2..1..1....1..1..0..0....3..2..0..3
%Y Column 1 is A000166(n-1).
%K nonn,tabl
%O 1,10
%A _R. H. Hardin_, Jan 04 2016