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%I #9 Aug 12 2016 06:55:35
%S 1,1,1,1,3,2,1,10,0,6,1,35,1,0,24,1,126,15,0,0,120,1,462,65,1,0,0,720,
%T 1,1716,202,22,0,0,0,5040,1,6435,537,396,1,0,0,0,40320,1,24310,1559,
%U 2516,30,0,0,0,0,362880,1,92378,6506,10533,1929,1,0,0,0,0,3628800,1,352716
%N T(n,k)=Number of nXk arrays containing k copies of 0..n-1 with every element equal to or 1 greater than any southwest or northwest neighbors modulo n and the upper left element equal to 0.
%C Table starts
%C ......1.1..1..1...1...1....1.....1......1........1.........1...........1
%C ......1.3.10.35.126.462.1716..6435..24310....92378....352716.....1352078
%C ......2.0..1.15..65.202..537..1559...6506....27557....104122......360598
%C ......6.0..0..1..22.396.2516.10533..33704....92526....369726.....2640466
%C .....24.0..0..0...1..30.1929.39176.359300..2137958...8673978....28057788
%C ....120.0..0..0...0...1...38..8314.552162.14897883.202307164..1740883167
%C ....720.0..0..0...0...0....1....46..29393..6837388.613275874.23205147788
%C ...5040.0..0..0...0...0....0.....1.....54....99680..77332028.23049149898
%C ..40320.0..0..0...0...0....0.....0......1.......62....376803...812885568
%C .362880.0..0..0...0...0....0.....0......0........1........70.....1268170
%H R. H. Hardin, <a href="/A267328/b267328.txt">Table of n, a(n) for n = 1..236</a>
%e Some solutions for n=3 k=4
%e ..0..1..2..0....0..1..1..2....0..0..1..2....0..0..1..2....0..1..2..0
%e ..0..1..2..2....0..0..1..2....2..0..1..2....2..0..1..1....1..1..2..0
%e ..1..1..2..0....2..0..1..2....2..0..1..1....2..0..1..2....0..1..2..2
%Y Column 1 is A000142(n-1).
%Y Row 2 is A001700(n-1).
%Y Row 3 is A267164.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jan 13 2016
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