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A233202 T(n,k)=Number of nXk 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabelled 8-colorings with no clashing color pairs).

%I A233202 #6 Jun 02 2025 08:52:35
%S A233202 1,1,1,3,3,3,11,36,36,11,48,528,1440,528,48,236,8256,62720,62720,8256,
%T A233202 236,1248,131328,2779136,7802880,2779136,131328,1248,6896,2098176,
%U A233202 123551744,981532672,981532672,123551744,2098176,6896,39168,33558528
%N A233202 T(n,k)=Number of nXk 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabelled 8-colorings with no clashing color pairs).
%C A233202 Table starts
%C A233202 ....1.......1..........3.............11................48...................236
%C A233202 ....1.......3.........36............528..............8256................131328
%C A233202 ....3......36.......1440..........62720...........2779136.............123551744
%C A233202 ...11.....528......62720........7802880.........981532672..........123833679872
%C A233202 ...48....8256....2779136......981532672......352524959744.......127365174788096
%C A233202 ..236..131328..123551744...123833679872...127365174788096....132364161848967168
%C A233202 .1248.2098176.5496242176.15635845218304.46111939268444160.138127371171167993856
%H A233202 R. H. Hardin, <a href="/A233202/b233202.txt">Table of n, a(n) for n = 1..180</a>
%F A233202 Empirical for column k:
%F A233202 k=1: a(n) = 12*a(n-1) -44*a(n-2) +48*a(n-3) for n>4
%F A233202 k=2: a(n) = 20*a(n-1) -64*a(n-2) for n>3
%F A233202 k=3: a(n) = 64*a(n-1) -960*a(n-2) +4096*a(n-3) for n>4
%F A233202 k=4: [order 5] for n>6
%F A233202 k=5: [order 10] for n>11
%F A233202 k=6: [order 22] for n>23
%e A233202 Some solutions for n=3 k=4
%e A233202 ..0..1..2..7....0..1..2..0....0..1..2..3....0..1..2..7....0..1..7..2
%e A233202 ..3..7..4..5....5..3..6..3....5..4..6..5....5..7..3..6....5..3..6..4
%e A233202 ..6..5..7..6....6..7..2..6....6..2..3..6....3..5..0..3....6..7..2..6
%Y A233202 Column 1 is A233162
%K A233202 nonn,tabl
%O A233202 1,4
%A A233202 _R. H. Hardin_, Dec 05 2013