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A211910 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.

%I A211910 #7 Jun 02 2025 07:51:40
%S A211910 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 A211910 6927,55822,14201,337,0,0,0,11296,605769,637721,51157,575,0,0,0,12732,
%U A211910 3997836,18239150,4639742,152650,919,0,0,0,12839,16321156,350026718,281228042
%N A211910 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 A211910 Table starts
%C A211910 ...0......0........0..........0............0............0.............0
%C A211910 ...2......2........0..........0............0............0.............0
%C A211910 ..10.....30.......41.........42...........42............0.............0
%C A211910 ..34....418.....2385.......6927........11296........12732.........12839
%C A211910 ..86...3006....55822.....605769......3997836.....16321156......41808669
%C A211910 .181..14201...637721...18239150....350026718...4630332478...42760973281
%C A211910 .337..51157..4639742..281228042..12075054829.379920664201.8940557439662
%C A211910 .575.152650.24871596.2788818593.228741733963
%H A211910 R. H. Hardin, <a href="/A211910/b211910.txt">Table of n, a(n) for n = 1..85</a>
%e A211910 Some solutions for n=4 k=4
%e A211910 ..0........0........0........0........0........0........0........0
%e A211910 ..1.2......1.2......1.2......1.2......1.0......1.2......1.2......1.2
%e A211910 ..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 A211910 ..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 A211910 nonn,tabl
%O A211910 1,3
%A A211910 _R. H. Hardin_ Apr 25 2012