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T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with the number of clockwise edge increases in every 2X2 subblock differing from each horizontal or vertical neighbor
9

%I #5 Mar 31 2012 12:37:06

%S 256,2120,2120,17920,34792,17920,151824,597288,597288,151824,1285076,

%T 10306944,22414008,10306944,1285076,10876432,177411808,843904488,

%U 843904488,177411808,10876432,92062852,3053150968,31625643196

%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with the number of clockwise edge increases in every 2X2 subblock differing from each horizontal or vertical neighbor

%C Table starts

%C .......256.........2120............17920..............151824

%C ......2120........34792...........597288............10306944

%C .....17920.......597288.........22414008...........843904488

%C ....151824.....10306944........843904488.........69248994984

%C ...1285076....177411808......31625643196.......5649505038240

%C ..10876432...3053150968....1185601231024.....461355684937208

%C ..92062852..52550629576...44457471151176...37682835967710128

%C .779221408.904498008200.1666962268642872.3077546846103277112

%H R. H. Hardin, <a href="/A205466/b205466.txt">Table of n, a(n) for n = 1..84</a>

%e Some solutions for n=4 k=3

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Jan 27 2012