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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)
12
1, 1, 3, 3, 8, 11, 10, 80, 80, 48, 36, 800, 2688, 896, 236, 136, 8576, 78336, 96256, 10496, 1248, 528, 92672, 2469888, 7938048, 3497984, 124928, 6896, 2080, 1009664, 76447744, 736362496, 808583168, 127533056, 1495040, 39168, 8256, 11018240
OFFSET
1,3
Table starts
....1.......1..........3............10................36..................136
....3.......8.........80...........800..............8576................92672
...11......80.......2688.........78336...........2469888.............76447744
...48.....896......96256.......7938048.........736362496..........65265467392
..236...10496....3497984.....808583168......221463445504.......56275748519936
.1248..124928..127533056...82428559360....66799223701504....48667983827959808
.6896.1495040.4653056000.8403942375424.20170789919653888.42129429039341895680
FORMULA
Empirical for column k:
k=1: a(n) = 12*a(n-1) -44*a(n-2) +48*a(n-3)
k=2: a(n) = 16*a(n-1) -48*a(n-2)
k=3: a(n) = 48*a(n-1) -448*a(n-2) +1024*a(n-3)
k=4: a(n) = 128*a(n-1) -2816*a(n-2) +16384*a(n-3)
k=5: [order 7]
k=6: [order 10]
k=7: [order 20]
Empirical for row n:
n=1: a(n) = 6*a(n-1) -8*a(n-2) for n>3
n=2: a(n) = 12*a(n-1) -128*a(n-3) for n>4
n=3: a(n) = 32*a(n-1) +64*a(n-2) -3072*a(n-3) +8192*a(n-4) for n>5
n=4: [order 7] for n>8
n=5: [order 10] for n>11
n=6: [order 24] for n>25
n=7: [order 47] for n>48
EXAMPLE
Some solutions for n=3 k=4
..0..1..0..2....0..1..2..5....0..1..2..4....0..1..5..2....0..1..2..1
..2..4..0..1....0..1..2..0....0..4..3..1....5..3..0..3....0..1..5..1
..5..1..5..4....5..1..3..5....3..4..5..4....5..4..5..3....0..4..2..4
CROSSREFS
Column 1 is A233162(n+1)
Column 2 is A233123
Column 3 is A233124
Row 1 is A007582(n-2)
Sequence in context: A300672 A368726 A052407 * A185350 A279910 A105039
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 05 2013
STATUS
approved

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Last modified September 20 13:01 EDT 2024. Contains 376072 sequences. (Running on oeis4.)