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%I #7 Aug 12 2016 06:55:35
%S 1,1,1,1,3,2,1,10,5,6,1,35,15,5,24,1,126,109,24,4,120,1,462,574,137,
%T 24,2,720,1,1716,2840,1138,293,3,4,5040,1,6435,13767,12214,2063,317,4,
%U 2,40320,1,24310,71646,104742,18276,6240,40,2,4,362880,1,92378,390862,741057
%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
%C ......1.3.10..35..126....462.....1716......6435.....24310.......92378
%C ......2.5.15.109..574...2840....13767.....71646....390862.....2170370
%C ......6.5.24.137.1138..12214...104742....741057...5022782....35540696
%C .....24.4.24.293.2063..18276...330969...5977624..79348962...830731810
%C ....120.2..3.317.6240..69265...663855..12954512.466131976.13687472182
%C ....720.4..4..40.8724.315356..4893787..55479601.912215513
%C ...5040.2..2...8.2416.605606.33284502.787556232
%C ..40320.4..4...8..136.275392.92367600
%C .362880.2..2...5....9..19113
%H R. H. Hardin, <a href="/A267278/b267278.txt">Table of n, a(n) for n = 1..126</a>
%e Some solutions for n=4 k=4
%e ..0..1..2..3....0..2..1..0....0..2..1..3....0..3..0..3....0..2..1..3
%e ..0..1..2..3....2..1..3..2....1..0..3..1....2..0..3..1....2..1..3..2
%e ..0..1..2..3....0..3..1..0....3..2..1..0....0..2..1..3....0..3..1..0
%e ..0..1..2..3....3..1..3..2....2..0..3..2....1..1..2..2....2..0..3..1
%Y Column 1 is A000142(n-1).
%Y Row 2 is A001700(n-1).
%Y Row 3 is A266573.
%Y Diagonal is A267018.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jan 12 2016