%I #5 Mar 31 2012 12:37:23
%S 1,2,2,5,12,5,15,152,159,15,52,3024,15215,3233,52,203,84124,2946848,
%T 3012383,90863,203,877,3057664,960563033,7289707650,992352688,3319375,
%U 877,4140,139056380,474608323506,35787552851324,36182978136598
%N T(n,k)=Number of nXk nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors
%C Table starts
%C ....1..........2...............5.................15..................52
%C ....2.........12.............152...............3024...............84124
%C ....5........159...........15215............2946848...........960563033
%C ...15.......3233.........3012383.........7289707650......35787552851324
%C ...52......90863.......992352688.....36182978136598.3233126493451564482
%C ..203....3319375....493060277544.314946169382603268
%C ..877..151329962.346279494967526
%C .4140.8361244271
%H R. H. Hardin, <a href="/A208581/b208581.txt">Table of n, a(n) for n = 1..48</a>
%e Some solutions for n=4 k=3
%e ..0..1..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..1
%e ..1..0..1....1..1..0....1..1..0....1..1..0....1..1..2....1..1..0....1..0..0
%e ..0..1..2....0..2..0....2..0..1....0..1..0....2..1..0....2..0..1....0..1..0
%e ..1..2..0....0..1..0....1..0..2....0..1..0....0..1..0....0..1..0....0..1..0
%Y Column 1 and row 1 are A000110
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_ Feb 29 2012