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T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X3 or 3X2 subblock having exactly one clockwise edge increases
9

%I #5 Mar 31 2012 12:37:14

%S 81,150,150,441,270,441,1416,552,552,1416,4371,1182,750,1182,4371,

%T 13386,2244,1272,1272,2244,13386,41589,4722,2094,2244,2094,4722,41589,

%U 128700,9582,3408,3408,3408,3408,9582,128700,397335,18930,5850,4836,4944,4836

%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X3 or 3X2 subblock having exactly one clockwise edge increases

%C Table starts

%C .....81...150..441..1416..4371.13386.41589.128700.397335.1229310.3802377

%C ....150...270..552..1182..2244..4722..9582..18930..39348...78804..159042

%C ....441...552..750..1272..2094..3408..5850...9792..15966...26880...45024

%C ...1416..1182.1272..2244..3408..4836..9144..13950..19752...36912...55944

%C ...4371..2244.2094..3408..4944..7584.13752..20208..31158...55920...81936

%C ..13386..4722.3408..4836..7584.11712.19200..30528..48096...78744..125184

%C ..41589..9582.5850..9144.13752.19200.35904..54528..77376..146304..223200

%C .128700.18930.9792.13950.20208.30528.54528..79104.121344..220032..323328

%H R. H. Hardin, <a href="/A207050/b207050.txt">Table of n, a(n) for n = 1..1624</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1) +a(n-2) +8*a(n-3) -2*a(n-4) for n>5

%F k=2: a(n) = 2*a(n-2) +5*a(n-3) -a(n-4) -a(n-5) for n>7

%F k=3: a(n) = 4*a(n-3) +a(n-4) for n>11

%F k=4: a(n) = 4*a(n-3) for n>12

%F k=5: a(n) = 4*a(n-3) for n>13

%F k=6: a(n) = 4*a(n-3) for n>14

%F k=7: a(n) = 4*a(n-3) for n>15

%F apparently a(n) = 4*a(n-3) for k>3 and n>k+8

%e Some solutions for n=4 k=3

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Feb 14 2012