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T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 1 0 0 horizontally and 0 0 1 and 1 0 1 vertically
10

%I #5 Mar 31 2012 12:37:29

%S 2,4,4,6,16,6,9,36,36,8,14,81,102,64,10,22,196,270,216,100,12,35,484,

%T 798,630,390,144,14,56,1225,2354,2156,1215,636,196,16,90,3136,7210,

%U 7128,4690,2079,966,256,18,145,8100,22232,24990,16830,8904,3276,1392,324,20,234

%N T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 1 0 0 horizontally and 0 0 1 and 1 0 1 vertically

%C Table starts

%C ..2...4....6....9....14.....22.....35......56.......90......145.......234

%C ..4..16...36...81...196....484...1225....3136.....8100....21025.....54756

%C ..6..36..102..270...798...2354...7210...22232....69570...218950....693810

%C ..8..64..216..630..2156...7128..24990...87136...311040..1112150...4018716

%C .10.100..390.1215..4690..16830..65765..251160...994050..3911375..15639390

%C .12.144..636.2079..8904..34012.145775..597856..2579940.10954895..47622744

%C .14.196..966.3276.15386..61754.287140.1247736..5805450.26247900.122620446

%C .16.256.1392.4860.24808.103664.518700.2364992.11769120.56106300.279344520

%H R. H. Hardin, <a href="/A209650/b209650.txt">Table of n, a(n) for n = 1..2828</a>

%F Empirical for column k:

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

%F k=2: a(n) = 4*n^2

%F k=3: a(n) = 2*n^3 + 6*n^2 - 2*n

%F k=4: a(n) = 9*n^3 + (9/2)*n^2 - (9/2)*n

%F k=5: a(n) = (7/2)*n^4 + 21*n^3 - (7/2)*n^2 - 7*n

%F k=6: a(n) = 22*n^4 + (88/3)*n^3 - 22*n^2 - (22/3)*n

%F k=7: a(n) = 7*n^5 + 70*n^4 + (35/3)*n^3 - (105/2)*n^2 - (7/6)*n

%e Some solutions for n=4 k=3

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

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

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

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

%Y Column 2 is A016742

%Y Column 3 is A086113

%Y Row 1 is A001611(n+2)

%Y Row 2 is A207436

%Y Row 3 is A207747

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Mar 11 2012