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T(n,k)=1/4 the number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock having one or three distinct clockwise edge differences
9

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

%S 33,313,313,2908,7653,2908,27129,183628,183628,27129,252951,4437262,

%T 11333893,4437262,252951,2358878,107248254,707627792,707627792,

%U 107248254,2358878,21997263,2593403383,44179487805,114628150378,44179487805

%N T(n,k)=1/4 the number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock having one or three distinct clockwise edge differences

%C Table starts

%C ........33...........313..............2908................27129

%C .......313..........7653............183628..............4437262

%C ......2908........183628..........11333893............707627792

%C .....27129.......4437262.........707627792.........114628150378

%C ....252951.....107248254.......44179487805.......18568897568014

%C ...2358878....2593403383.....2759914868891.....3010470408635630

%C ..21997263...62718516080...172422974616663...488107505505461510

%C .205132657.1516857228897.10772379159246366.79144584564609543464

%H R. H. Hardin, <a href="/A210077/b210077.txt">Table of n, a(n) for n = 1..144</a>

%e Some solutions for n=4 k=3

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Mar 17 2012