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A208096 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 horizontal, diagonal or antidiagonal neighbor (colorings ignoring permutations of colors).

%I A208096 #21 Mar 13 2023 13:31:21
%S A208096 1,1,2,2,4,5,5,30,34,15,15,377,1573,500,52,52,7239,169064,192328,
%T A208096 10900,203,203,193228,34438557,235862938,43366459,322768,877,877,
%U A208096 6752442,11535531783,677352910013,746823293346,15769674462,12297768,4140
%N A208096 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 horizontal, diagonal or antidiagonal neighbor (colorings ignoring permutations of colors).
%H A208096 Andrew Howroyd, <a href="/A208096/b208096.txt">Table of n, a(n) for n = 1..210</a> (terms 1..39 from R. H. Hardin).
%e A208096 Table starts
%e A208096 ....1........1...........2............5...........15..........52...........203
%e A208096 ....2........4..........30..........377.........7239......193228.......6752442
%e A208096 ....5.......34........1573.......169064.....34438557.11535531783.5804338800147
%e A208096 ...15......500......192328....235862938.677352910013
%e A208096 ...52....10900....43366459.746823293346
%e A208096 ..203...322768.15769674462
%e A208096 ..877.12297768
%e A208096 .4140
%e A208096 Some solutions for n=4 k=3
%e A208096 ..0..1..2....0..1..0....0..1..0....0..1..2....0..1..2....0..1..0....0..1..0
%e A208096 ..0..1..2....2..1..0....0..1..0....0..3..2....0..3..0....2..3..0....0..1..0
%e A208096 ..0..1..0....3..1..2....2..1..0....0..1..0....0..1..0....0..3..0....2..1..2
%e A208096 ..0..1..0....2..1..0....2..1..2....3..1..0....0..3..0....0..1..0....0..1..0
%Y A208096 Columns 1..5 are A000110, A207864, A208093, A208094, A208095.
%Y A208096 Rows 1..5 are A000110(n-1), A208097, A208098, A208099, A208100.
%Y A208096 Main diagonal is A361449.
%Y A208096 Cf. A207868.
%K A208096 nonn,tabl
%O A208096 1,3
%A A208096 _R. H. Hardin_, Feb 23 2012