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T(n,k)=Number of lower triangular n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any horizontal or vertical neighbor, and containing the value n(n+1)/2-k-1
6

%I #5 Dec 18 2015 18:18:09

%S 0,0,2,0,2,10,0,0,30,34,0,0,41,418,86,0,0,42,2385,3006,181,0,0,42,

%T 6927,55822,14201,337,0,0,0,11296,605769,637721,51157,575,0,0,0,12732,

%U 3997836,18239150,4639742,152650,919,0,0,0,12839,16321156,350026718,281228042

%N T(n,k)=Number of lower triangular n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any horizontal or vertical neighbor, and containing the value n(n+1)/2-k-1

%C Table starts

%C ...0......0........0..........0............0............0.............0

%C ...2......2........0..........0............0............0.............0

%C ..10.....30.......41.........42...........42............0.............0

%C ..34....418.....2385.......6927........11296........12732.........12839

%C ..86...3006....55822.....605769......3997836.....16321156......41808669

%C .181..14201...637721...18239150....350026718...4630332478...42760973281

%C .337..51157..4639742..281228042..12075054829.379920664201.8940557439662

%C .575.152650.24871596.2788818593.228741733963

%H R. H. Hardin, <a href="/A211910/b211910.txt">Table of n, a(n) for n = 1..85</a>

%e Some solutions for n=4 k=4

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

%e ..1.2......1.2......1.2......1.2......1.0......1.2......1.2......1.2

%e ..0.3.4....3.4.2....2.3.4....2.3.4....2.3.4....3.4.0....3.1.4....3.4.0

%e ..1.0.5.3..5.6.5.0..1.5.6.4..4.5.0.4..5.4.6.0..4.2.5.3..4.5.1.6..4.3.5.4

%K nonn,tabl

%O 1,3

%A _R. H. Hardin_ Apr 25 2012