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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 west, northeast or northwest neighbor modulo n and the upper left element equal to 0.
5

%I #5 Aug 12 2016 06:55:34

%S 1,1,1,1,0,2,1,0,2,6,1,0,2,23,24,1,0,2,126,907,120,1,0,2,943,67735,

%T 51499,720,1,0,5,8360,6597969,45049091,4161843,5040,1,0,14,87289,

%U 763867475,55872746031,53041447974,447189962,40320,1,0,44,1073932,98274481798

%N T(n,k)=Number of nXk arrays containing k copies of 0..n-1 with no element 1 greater than its west, northeast 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 .....1.........0...........0...........0.........0...........0.......0..0.0

%C .....2.........2...........2...........2.........2...........5......14.44

%C .....6........23.........126.........943......8360.......87289.1073932

%C ....24.......907.......67735.....6597969.763867475.98274481798

%C ...120.....51499....45049091.55872746031

%C ...720...4161843.53041447974

%C ..5040.447189962

%C .40320

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 1 is A000142(n-1).

%K nonn,tabl

%O 1,6

%A _R. H. Hardin_, Jan 08 2016