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%I #5 Mar 31 2012 12:36:22
%S 1,5,5,16,96,47,36,775,4322,849,69,3638,132214,571364,29241,117,12438,
%T 1674043,86867366,205801866,1901849,184,34247,12561823,3703163910,
%U 214726600125,202803700252,234932757,272,82057,66369488,73569838704
%N T(n,k)=Half the number of lower triangles of an (n+1)X(n+1) 0..k array with no element equal to the average of its horizontal and vertical neighbors
%C Table starts
%C .................1.......................5........................16
%C .................5......................96.......................775
%C ................47....................4322....................132214
%C ...............849..................571364..................86867366
%C .............29241...............205801866..............214726600125
%C ...........1901849............202803700252..........1988649454264015
%C .........234932757.........547917448108462......69098146174647014753
%C .......55047807551.....4059864930297777162.9010212831798851496619501
%C ....24470603864937.82468548660331834255159
%C .20637055514911557
%H R. H. Hardin, <a href="/A194615/b194615.txt">Table of n, a(n) for n = 1..61</a>
%e Some solutions for 4X4
%e ..2........0........0........2........2........0........0........0
%e ..0.0......1.1......2.0......1.1......0.0......2.0......1.0......1.2
%e ..0.1.0....0.0.2....1.2.2....2.0.0....1.1.1....2.2.0....0.0.1....2.1.1
%e ..2.2.1.0..2.2.2.0..2.1.0.2..1.2.2.1..1.0.2.1..1.2.2.0..1.0.1.0..1.1.0.2
%Y Column 1 is A140422(n+1)
%Y Row 1 is A055232(n+1)
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_ Aug 30 2011
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