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

Author

R. H. Hardin, Dec 05 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A233162(n+1)

Column 2 is A233123

Column 3 is A233124

Row 1 is A007582(n-2)

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