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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 neighbor modulo n and the upper left element equal to 0.
7

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

%S 1,1,1,1,1,2,1,1,7,6,1,1,39,171,24,1,1,265,8190,6666,120,1,1,1802,

%T 442285,3264584,384360,720,1,1,12239,25839438,1935720551,2357929910,

%U 30900150,5040,1,1,84614,1605405629,1294905380013,18647592370365,2805027363620

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

%C Table starts

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

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

%C ...2......7.........39............265...............1802..................12239

%C ...6....171.......8190.........442285...........25839438.............1605405629

%C ..24...6666....3264584.....1935720551......1294905380013........934699483462236

%C .120.384360.2357929910.18647592370365.170964048684610518.1721790755351199712746

%H R. H. Hardin, <a href="/A266309/b266309.txt">Table of n, a(n) for n = 1..66</a>

%e Some solutions for n=3 k=4

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

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

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

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

%K nonn,tabl

%O 1,6

%A _R. H. Hardin_, Dec 26 2015