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A208301 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 or antidiagonal neighbor (colorings ignoring permutations of colors).

%I A208301 #11 Mar 13 2023 13:31:13
%S A208301 1,1,2,2,5,5,5,42,52,15,15,602,2906,877,52,52,12840,373780,433252,
%T A208301 21147,203,203,373780,87852626,656404264,113503692,678570,877,877,
%U A208301 14050312,33093356640,2227156082842,2475181138384,46538017584,27644437,4140
%N A208301 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 or antidiagonal neighbor (colorings ignoring permutations of colors).
%H A208301 Andrew Howroyd, <a href="/A208301/b208301.txt">Table of n, a(n) for n = 1..210</a> (terms 1..58 from R. H. Hardin)
%e A208301 Table starts
%e A208301 ....1..........1.................2.....................5
%e A208301 ....2..........5................42...................602
%e A208301 ....5.........52..............2906................373780
%e A208301 ...15........877............433252.............656404264
%e A208301 ...52......21147.........113503692.........2475181138384
%e A208301 ..203.....678570.......46538017584.....17131843186425504
%e A208301 ..877...27644437....27700815674032.196551307092757144384
%e A208301 .4140.1382958545.22702140562948192
%e A208301 Some solutions for n=4 k=3
%e A208301 ..0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..2....0..1..0
%e A208301 ..0..1..0....0..1..0....0..1..0....0..1..0....2..3..0....0..3..0....0..1..0
%e A208301 ..0..1..0....0..2..1....0..1..0....0..1..0....0..2..0....0..1..0....2..1..0
%e A208301 ..0..2..1....0..2..0....0..1..0....0..1..2....0..1..0....0..3..0....2..1..2
%Y A208301 Columns 1..6 are A000110, A099977(n-1), A208297, A208298, A208299, A208300
%Y A208301 Rows 1..7 are A000110(n-1), A208302, A208303, A208305, A208305, A208306, A208307.
%Y A208301 Main diagonal is A361450.
%Y A208301 Cf. A207868.
%K A208301 nonn,tabl
%O A208301 1,3
%A A208301 _R. H. Hardin_, Feb 25 2012