A233256 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 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, 10, 11, 10, 104, 136, 48, 36, 1184, 4672, 2080, 236, 136, 13952, 166400, 221696, 32896, 1248, 528, 166400, 6049792, 23896064, 10620928, 524800, 6896, 2080, 1992704, 220626944, 2647261184, 3439984640, 509640704, 8390656, 39168, 8256

Offset: 1

Author

R. H. Hardin, Dec 06 2013

Keywords

• nonn
• tabl

Comments

Table starts

.......1...........1................3....................10

.......3..........10..............104..................1184

......11.........136.............4672................166400

......48........2080...........221696..............23896064

.....236.......32896.........10620928............3439984640

....1248......524800........509640704..........495341010944

....6896.....8390656......24461443072........71328837140480

...39168...134225920....1174138781696.....10271348253261824

..226496..2147516416...56358577635328...1479074079750225920

.1325568.34359869440.2705211055407104.212986666384520904704

Examples

			Some solutions for n=3 k=4
..0..1..0..2....0..1..0..2....0..1..2..4....0..1..0..2....0..1..2..4
..5..3..5..2....2..1..0..4....3..4..2..4....3..4..0..4....2..0..3..1
..4..3..1..5....5..2..0..3....3..1..5..4....3..1..5..1....4..0..2..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..240

Crossrefs

Column 1 is A233162(n+1)

Column 2 is A026244(n-1)

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) = 20*a(n-1) -64*a(n-2)

k=3: a(n) = 56*a(n-1) -384*a(n-2)

k=4: a(n) = 160*a(n-1) -2304*a(n-2)

k=5: a(n) = 512*a(n-1) -33792*a(n-2) +589824*a(n-3)

k=6: a(n) = 1664*a(n-1) -471040*a(n-2) [phone]*a(n-3) -1358954496*a(n-4)

k=7: [order 5]

Empirical for row n:

n=1: a(n) = 6*a(n-1) -8*a(n-2) for n>3

n=2: a(n) = 16*a(n-1) -48*a(n-2) for n>3

n=3: a(n) = 48*a(n-1) -448*a(n-2) +1024*a(n-3) for n>5

n=4: a(n) = 160*a(n-1) -6144*a(n-2) +86016*a(n-3) -393216*a(n-4) for n>8

n=5: [order 7] for n>11

n=6: [order 10] for n>16

n=7: [order 28] for n>34