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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 or southwest neighbor modulo n and the upper left element equal to 0.
6

%I #6 Aug 12 2016 06:55:34

%S 1,1,1,1,0,2,1,0,2,6,1,0,6,44,24,1,0,31,1129,1949,120,1,0,141,30637,

%T 437427,119544,720,1,0,550,775567,109852687,310439601,9966710,5040,1,

%U 0,2046,21970109,31745527110,1011979038956,368078731163,1094087602,40320,1

%N T(n,k)=Number of nXk arrays containing k copies of 0..n-1 with no element 1 greater than its west or southwest neighbor modulo n and the upper left element equal to 0.

%C Table starts

%C ...1.......1............1.................1................1..............1

%C ...1.......0............0.................0................0..............0

%C ...2.......2............6................31..............141............550

%C ...6......44.........1129.............30637...........775567.......21970109

%C ..24....1949.......437427.........109852687......31745527110.10164842993183

%C .120..119544....310439601.....1011979038956.3899321211077068

%C .720.9966710.368078731163.18398910840846332

%H R. H. Hardin, <a href="/A267072/b267072.txt">Table of n, a(n) for n = 1..60</a>

%e Some solutions for n=4 k=4

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

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

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

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

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

%K nonn,tabl

%O 1,6

%A _R. H. Hardin_, Jan 10 2016