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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
11

%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