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)

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

Comments

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

Links

R. H. Hardin, Table of n, a(n) for n = 1..287

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

Adjacent sequences: A233171 A233172 A233173 * A233175 A233176 A233177

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 05 2013

Status

approved