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A233174 T(n,k)=Number of nXk 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

%I A233174 #6 Jun 02 2025 08:51:46
%S A233174 1,1,3,3,8,11,10,80,80,48,36,800,2688,896,236,136,8576,78336,96256,
%T A233174 10496,1248,528,92672,2469888,7938048,3497984,124928,6896,2080,
%U A233174 1009664,76447744,736362496,808583168,127533056,1495040,39168,8256,11018240
%N A233174 T(n,k)=Number of nXk 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).
%C A233174 Table starts
%C A233174 ....1.......1..........3............10................36..................136
%C A233174 ....3.......8.........80...........800..............8576................92672
%C A233174 ...11......80.......2688.........78336...........2469888.............76447744
%C A233174 ...48.....896......96256.......7938048.........736362496..........65265467392
%C A233174 ..236...10496....3497984.....808583168......221463445504.......56275748519936
%C A233174 .1248..124928..127533056...82428559360....66799223701504....48667983827959808
%C A233174 .6896.1495040.4653056000.8403942375424.20170789919653888.42129429039341895680
%H A233174 R. H. Hardin, <a href="/A233174/b233174.txt">Table of n, a(n) for n = 1..287</a>
%F A233174 Empirical for column k:
%F A233174 k=1: a(n) = 12*a(n-1) -44*a(n-2) +48*a(n-3)
%F A233174 k=2: a(n) = 16*a(n-1) -48*a(n-2)
%F A233174 k=3: a(n) = 48*a(n-1) -448*a(n-2) +1024*a(n-3)
%F A233174 k=4: a(n) = 128*a(n-1) -2816*a(n-2) +16384*a(n-3)
%F A233174 k=5: [order 7]
%F A233174 k=6: [order 10]
%F A233174 k=7: [order 20]
%F A233174 Empirical for row n:
%F A233174 n=1: a(n) = 6*a(n-1) -8*a(n-2) for n>3
%F A233174 n=2: a(n) = 12*a(n-1) -128*a(n-3) for n>4
%F A233174 n=3: a(n) = 32*a(n-1) +64*a(n-2) -3072*a(n-3) +8192*a(n-4) for n>5
%F A233174 n=4: [order 7] for n>8
%F A233174 n=5: [order 10] for n>11
%F A233174 n=6: [order 24] for n>25
%F A233174 n=7: [order 47] for n>48
%e A233174 Some solutions for n=3 k=4
%e A233174 ..0..1..0..2....0..1..2..5....0..1..2..4....0..1..5..2....0..1..2..1
%e A233174 ..2..4..0..1....0..1..2..0....0..4..3..1....5..3..0..3....0..1..5..1
%e A233174 ..5..1..5..4....5..1..3..5....3..4..5..4....5..4..5..3....0..4..2..4
%Y A233174 Column 1 is A233162(n+1)
%Y A233174 Column 2 is A233123
%Y A233174 Column 3 is A233124
%Y A233174 Row 1 is A007582(n-2)
%K A233174 nonn,tabl
%O A233174 1,3
%A A233174 _R. H. Hardin_, Dec 05 2013