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T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with each 3X3 subblock having clockwise perimeter pattern 00000001 00000011 or 00001001
9

%I #4 Jul 22 2015 11:49:35

%S 48,104,104,274,201,274,560,544,544,560,966,1145,1336,1145,966,2300,

%T 1524,2966,2966,1524,2300,4762,3591,3764,5629,3764,3591,4762,8252,

%U 8550,8660,7146,7146,8660,8550,8252,17470,13055,21028,19157,10952,19157,21028

%N T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with each 3X3 subblock having clockwise perimeter pattern 00000001 00000011 or 00001001

%C Table starts

%C ....48...104....274....560....966....2300....4762....8252....17470....38160

%C ...104...201....544...1145...1524....3591....8550...13055....24762....60761

%C ...274...544...1336...2966...3764....8660...21028...33108....60116...153106

%C ...560..1145...2966...5629...7146...19157...45596...64925...134780...364807

%C ...966..1524...3764...7146..10952...29166...62980..101512...225924...560690

%C ..2300..3591...8660..19157..29166...72652..168582..292171...625218..1609460

%C ..4762..8550..21028..45596..62980..168582..385280..635774..1454932..3865506

%C ..8252.13055..33108..64925.101512..292171..635774.1076482..2711612..7110332

%C .17470.24762..60116.134780.225924..625218.1454932.2711612..6847376.18585578

%C .38160.60761.153106.364807.560690.1609460.3865506.7110332.18585578.52370322

%H R. H. Hardin, <a href="/A260294/b260294.txt">Table of n, a(n) for n = 1..544</a>

%F Empirical for column k:

%F k=1: [linear recurrence of order 9] for n>10

%F k=2: [order 10] for n>12

%F k=3: [order 24] for n>28

%F k=4: [order 40] for n>44

%F k=5: [order 72] for n>78

%e Some solutions for n=4 k=4

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

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jul 22 2015