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%I #6 Dec 18 2015 18:17:44
%S 1,1,2,1,3,0,1,3,6,0,1,3,24,0,0,1,3,33,192,0,0,1,3,34,1620,1152,0,0,1,
%T 3,34,3936,136080,5760,0,0,1,3,34,5249,1797696,17962560,26880,0,0,1,3,
%U 34,5556,7418424,2054111040,3751608960,118272,0,0,1,3,34,5586,15005952
%N T(n,k)=Number of lower triangles of an n X n 0..k array with new values introduced in row major order 0..k and no two horizontal or vertical neighbors of any element equal
%C Table starts
%C .1.1......1.............1.................1...............1.................1
%C .2.3......3.............3.................3...............3.................3
%C .0.6.....24............33................34..............34................34
%C .0.0....192..........1620..............3936............5249..............5556
%C .0.0...1152........136080...........1797696.........7418424..........15005952
%C .0.0...5760......17962560........2054111040.....41521783200......282616583760
%C .0.0..26880....3751608960.....5741390328960.788547395813440.24289270603904160
%C .0.0.118272.1233597237120.39210440893622016
%H R. H. Hardin, <a href="/A194893/b194893.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......0.1......1.2......0.1......1.2......1.2
%e ..1.3.3....1.2.3....3.0.0....2.3.0....3.3.1....2.3.4....3.0.4....3.2.0
%e ..4.4.0.2..4.0.1.4..4.1.3.2..1.4.4.2..2.0.1.3..4.0.2.3..2.0.1.2..4.4.0.3
%K nonn,tabl
%O 1,3
%A _R. H. Hardin_ Sep 04 2011
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