%I #9 Mar 15 2023 16:27:02
%S 1,2,2,5,7,5,15,67,67,15,52,1080,4192,1080,52,203,25287,587208,587208,
%T 25287,203,877,794545,147512732,953124784,147512732,794545,877,4140,
%U 31858034,58668937932,3410310590912,3410310590912,58668937932,31858034
%N T(n,k)=Number of n X k nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any diagonal or antidiagonal neighbor (colorings ignoring permutations of colors).
%H Andrew Howroyd, <a href="/A207981/b207981.txt">Table of n, a(n) for n = 1..496</a> (terms 1..40 from R. H. Hardin).
%e Table starts
%e ....1........2...........5............15............52...............203
%e ....2........7..........67..........1080.........25287............794545
%e ....5.......67........4192........587208.....147512732.......58668937932
%e ...15.....1080......587208.....953124784.3410310590912.22727131144960768
%e ...52....25287...147512732.3410310590912
%e ..203...794545.58668937932
%e ..877.31858034
%e .4140
%e ...
%e Some solutions for n=4 k=3
%e ..0..0..0....0..0..1....0..0..0....0..0..0....0..1..0....0..0..0....0..0..0
%e ..1..1..1....1..2..1....1..1..1....1..1..1....2..1..0....1..2..1....1..1..1
%e ..2..0..2....1..2..0....0..0..2....0..0..0....0..1..3....0..0..0....2..2..0
%e ..1..0..1....0..2..0....1..1..1....1..1..1....0..4..0....2..1..1....0..1..0
%Y Columns 1..4 are A000110, A207978, A207979, A207980.
%Y Main diagonal is A361452.
%Y Cf. A207868.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Feb 22 2012