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%I #8 Aug 12 2016 06:55:34
%S 1,1,1,1,3,2,1,10,5,6,1,35,15,8,24,1,126,59,21,11,120,1,462,257,137,
%T 45,15,720,1,1716,1205,759,259,37,19,5040,1,6435,5879,4835,2063,537,
%U 147,24,40320,1,24310,29693,31591,18157,5493,1015,62,29,362880,1,92378,153097
%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 northeast 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...59....257.....1205......5879.....29693.....153097.....806375
%C ......6..8..21..137....759.....4835.....31591....216460....1516047...10864196
%C .....24.11..45..259...2063....18157....172169...1717333...17555313..184061791
%C ....120.15..37..537...5493....69265....912057..13122646..193577805.2965487933
%C ....720.19.147.1015..15171...255437...4893787.100710495.2166450939
%C ...5040.24..62.2132..39804...997598..26320280.787556232
%C ..40320.29.537.4045.117871..3689017.143694547
%C .362880.35.104.8511.292196.14484099
%H R. H. Hardin, <a href="/A267019/b267019.txt">Table of n, a(n) for n = 1..126</a>
%e Some solutions for n=4 k=4
%e ..0..2..3..2....0..1..3..2....0..1..3..2....0..3..1..2....0..3..0..2
%e ..2..0..2..0....2..0..2..0....2..0..2..0....3..1..3..1....3..1..3..1
%e ..1..3..1..3....1..3..1..3....0..3..1..2....2..0..2..0....2..0..1..3
%e ..0..1..3..1....3..2..0..1....3..1..3..1....0..2..1..3....1..2..0..2
%Y Column 1 is A000142(n-1).
%Y Column 2 is A024206(n+1).
%Y Row 2 is A001700(n-1).
%Y Row 3 is A266682.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jan 09 2016
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