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Number of nX3 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
1

%I #5 Mar 31 2012 12:37:23

%S 5,152,15215,3012383,992352688,493060277544,346279494967526,

%T 328147828693412793,405140655255049613481,634030553946045902705124,

%U 1230184720940057735002661377,2905785104106201330409269721974

%N Number of nX3 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 Column 3 of A208581

%H R. H. Hardin, <a href="/A208578/b208578.txt">Table of n, a(n) for n = 1..40</a>

%e Some solutions for n=4

%e ..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..1....0..0..0

%e ..1..1..0....1..1..0....1..2..1....1..1..0....1..1..0....1..0..0....1..1..0

%e ..2..0..1....2..0..1....0..0..0....0..1..0....0..2..1....0..1..0....0..1..0

%e ..0..1..0....1..0..2....3..1..0....0..1..0....0..0..0....0..1..0....0..1..2

%K nonn

%O 1,1

%A _R. H. Hardin_ Feb 29 2012