%I #5 Dec 18 2015 18:18:09
%S 0,0,2,0,2,9,0,0,23,31,0,0,27,340,80,0,0,27,1685,2577,171,0,0,27,4151,
%T 43607,12616,322,0,0,0,5809,425384,529891,46582,554,0,0,0,6093,
%U 2484024,14087170,4014522,141478,891,0,0,0,6097,8826873,249499909,230476122
%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, vertical or antidiagonal 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 ...9.....23.......27.........27...........27..............0.............0
%C ..31....340.....1685.......4151.........5809...........6093..........6097
%C ..80...2577....43607.....425384......2484024........8826873......19472124
%C .171..12616...529891...14087170....249499909.....3020833719...25290834411
%C .322..46582..4014522..230476122...9339489832...276214923832.6082437511849
%C .554.141478.22135982.2379082308.186659686448.11092305676290
%H R. H. Hardin, <a href="/A211930/b211930.txt">Table of n, a(n) for n = 1..86</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......1.2......1.2......1.2......1.0
%e ..3.4.5....3.4.1....0.3.4....0.3.4....3.4.1....0.3.4....3.0.4....2.3.1
%e ..6.7.0.6..5.3.0.6..2.5.2.4..1.5.1.4..5.0.2.4..1.5.3.4..5.6.2.4..0.4.5.0
%K nonn,tabl
%O 1,3
%A _R. H. Hardin_ Apr 25 2012