The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #7 Dec 13 2015 18:47:34
%S 81,399,399,1620,2577,1620,6462,14781,14781,6462,26481,91674,141759,
%T 91674,26481,110769,594348,1419921,1419921,594348,110769,469617,
%U 3902463,14528199,22647363,14528199,3902463,469617,2009553,25900263,150387285
%N T(n,k) = number of (n+1) X (k+1) 0..2 arrays with the number of clockwise edge increases in 2 X 2 subblocks nondecreasing, and counterclockwise edge increases nonincreasing, rightwards and downwards.
%C Table starts
%C ......81.......399........1620..........6462...........26481............110769
%C .....399......2577.......14781.........91674..........594348...........3902463
%C ....1620.....14781......141759.......1419921........14528199.........150387285
%C ....6462.....91674.....1419921......22647363.......369441411........6062752884
%C ...26481....594348....14528199.....369441411......9567269487......249853070682
%C ..110769...3902463...150387285....6062752884....249853070682....10370489275269
%C ..469617..25900263..1567749888..100259781690...6556642024200...433165769694465
%C .2009553.172835859.16417626507.1661323349889.172503406693200.18115074102295746
%H R. H. Hardin, <a href="/A206542/b206542.txt">Table of n, a(n) for n = 1..179</a>
%e Some solutions for n=4, k=3:
%e ..0..1..0..0....2..2..0..0....1..1..2..1....0..0..2..2....1..0..2..0
%e ..0..0..0..2....2..0..0..2....1..2..2..2....0..2..2..0....2..1..0..1
%e ..0..1..0..0....2..0..2..2....1..1..2..0....2..2..0..0....0..2..1..0
%e ..0..0..0..1....0..0..2..1....2..1..1..1....2..0..0..1....1..0..2..1
%e ..1..0..2..2....2..2..2..1....2..1..0..2....2..2..2..1....2..1..0..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 09 2012