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%I #7 Dec 11 2015 21:27:07
%S 256,1976,1976,15616,19688,15616,124048,205804,205804,124048,986388,
%T 2410188,3802676,2410188,986388,7854572,30417316,95187756,95187756,
%U 30417316,7854572,62623348,406202048,2674444796,5674969344,2674444796
%N T(n,k) = number of (n+1) X (k+1) 0..3 arrays with every 2 X 2 subblock having the same number of clockwise edge increases as its horizontal neighbors and the same number of counterclockwise edge increases as its vertical neighbors.
%C Table starts
%C .......256........1976..........15616.............124048................986388
%C ......1976.......19688.........205804............2410188..............30417316
%C .....15616......205804........3802676...........95187756............2674444796
%C ....124048.....2410188.......95187756.........5674969344..........364197868292
%C ....986388....30417316.....2674444796.......364197868292........51975660472496
%C ...7854572...406202048....78597249508.....23825180259760......7481908870312588
%C ..62623348..5614757320..2345626036136...1565902419680820...1078848431799509828
%C .499915248.79279051900.70435464744476.103072965502712948.155633082985105845972
%H R. H. Hardin, <a href="/A206188/b206188.txt">Table of n, a(n) for n = 1..84</a>
%e Some solutions for n=4, k=3:
%e ..1..0..0..0....3..2..0..0....2..0..2..2....2..3..2..0....0..2..0..3
%e ..0..3..2..1....2..1..3..1....3..0..0..0....2..3..0..0....0..2..0..3
%e ..0..2..2..1....0..3..2..2....0..3..2..1....0..0..2..1....2..2..0..3
%e ..0..1..1..1....3..2..0..3....0..2..2..1....3..0..1..1....0..2..0..3
%e ..1..0..3..2....1..2..3..3....0..1..1..1....2..2..0..2....2..2..0..3
%Y Column 1 is A205363.
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 04 2012