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T(n,k)=Number of nXk arrays containing k copies of 0..n-1 with no element plus any diagonal or antidiagonal neighbor equal to n-1.
4

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

%S 1,1,2,1,2,6,1,2,22,24,1,2,88,384,120,1,2,296,7768,19080,720,1,2,1372,

%T 226296,4027960,1019328,5040,1,2,6128,7089448,1203241488,2437859280,

%U 106546608,40320,1,2,29552,253282792,409870443648,8822224268688

%N T(n,k)=Number of nXk arrays containing k copies of 0..n-1 with no element plus any diagonal or antidiagonal neighbor equal to n-1.

%C Table starts

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

%C ......2...........2.............2.............2............2.........2

%C ......6..........22............88...........296.........1372......6128

%C .....24.........384..........7768........226296......7089448.253282792

%C ....120.......19080.......4027960....1203241488.409870443648

%C ....720.....1019328....2437859280.8822224268688

%C ...5040...106546608.3971117183616

%C ..40320.11075595648

%C .362880

%H R. H. Hardin, <a href="/A266183/b266183.txt">Table of n, a(n) for n = 1..49</a>

%e Some solutions for n=3 k=4

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

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

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

%Y Column 1 is A000142.

%Y Column 2 is A265860.

%K nonn,tabl

%O 1,3

%A _R. H. Hardin_, Dec 23 2015