%I #5 Mar 31 2012 12:37:10
%S 14,45,45,162,130,162,594,336,336,594,2268,992,760,992,2268,8802,2996,
%T 2224,2224,2996,8802,34236,9072,5632,8136,5632,9072,34236,133974,
%U 27656,14416,21984,21984,14416,27656,133974,525636,84152,40032,74080,86152
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X3 or 3X2 subblock having exactly two equal edges, and new values 0..2 introduced in row major order
%C Table starts
%C .....14....45....162....594....2268.....8802.....34236.....133974......525636
%C .....45...130....336....992....2996.....9072.....27656......84152......256416
%C ....162...336....760...2224....5632....14416.....40032.....101376......259488
%C ....594...992...2224...8136...21984....74080....274320.....747456.....2518720
%C ...2268..2996...5632..21984...86152...359424...1435584....5673232....23721984
%C ...8802..9072..14416..74080..359424..1764000...9438912...46540800...228988224
%C ..34236.27656..40032.274320.1435584..9438912..68074272..366583680..2427719040
%C .133974.84152.101376.747456.5673232.46540800.366583680.2870491680.23806365696
%H R. H. Hardin, <a href="/A206215/b206215.txt">Table of n, a(n) for n = 1..840</a>
%F Empirical for column k:
%F k=1: a(n) = 4*a(n-1) -a(n-2) +12*a(n-3) -36*a(n-4) for n>5
%F k=2: a(n) = a(n-1) +6*a(n-2) +4*a(n-3) -10*a(n-4) for n>6
%F k=3: a(n) = 18*a(n-3) for n>6
%F k=4: a(n) = 34*a(n-3) for n>7
%F k=5: a(n) = 66*a(n-3) for n>8
%F k=6: a(n) = 130*a(n-3) for n>9
%F k=7: a(n) = 258*a(n-3) for n>10
%F apparently a(n) = (2^(k+1) +2)*a(n-3) for k>2 and n>k+3
%e Some solutions for n=4 k=3
%e ..0..1..0..2....0..0..1..2....0..0..1..2....0..0..1..0....0..0..1..1
%e ..1..0..0..2....2..0..0..1....0..1..2..2....0..1..0..0....2..2..0..1
%e ..0..0..1..0....0..2..0..0....1..2..2..0....1..0..0..2....0..2..2..0
%e ..0..2..0..0....0..0..1..0....2..2..0..1....0..0..1..0....1..0..2..2
%e ..2..0..0..1....1..0..0..1....2..0..1..1....0..1..0..0....1..1..0..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Feb 04 2012