%I #4 Jun 29 2015 15:27:18

%S 11,31,31,87,129,87,245,533,533,245,689,2219,3270,2219,689,1939,9227,

%T 20293,20293,9227,1939,5455,38409,126045,189211,126045,38409,5455,

%U 15349,159845,784130,1769635,1769635,784130,159845,15349,43185,665339,4879059

%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with each 2X2 subblock having clockwise pattern 0000 0001 0101 0111

%C Table starts

%C .....11.......31.........87..........245............689.............1939

%C .....31......129........533.........2219...........9227............38409

%C .....87......533.......3270........20293.........126045...........784130

%C ....245.....2219......20293.......189211........1769635.........16602297

%C ....689.....9227.....126045......1769635.......25009044........355119489

%C ...1939....38409.....784130.....16602297......355119489.......7648655920

%C ...5455...159845....4879059....155863519.....5050441910.....165145291429

%C ..15349...665339...30366347...1464104971....71892362811....3570854380319

%C ..43185..2769251..189000090..13754727159..1023722858631...77252441141038

%C .121507.11526489.1176388523.129236342101.14580213573278.1671822431529063

%H R. H. Hardin, <a href="/A259515/b259515.txt">Table of n, a(n) for n = 1..419</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1) +3*a(n-2) -2*a(n-3)

%F k=2: a(n) = 2*a(n-1) +11*a(n-2) -4*a(n-3) -18*a(n-4)

%F k=3: [order 10]

%F k=4: [order 14]

%F k=5: [order 36]

%F k=6: [order 56]

%e Some solutions for n=4 k=4

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jun 29 2015