A233256 - OEIS

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

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,3

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

LINKS

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

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) +44826624*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

EXAMPLE

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

CROSSREFS

Column 1 is A233162(n+1)

Column 2 is A026244(n-1)

Row 1 is A007582(n-2)

Sequence in context: A124630 A321397 A128015 * A332955 A355089 A218953

Adjacent sequences: A233253 A233254 A233255 * A233257 A233258 A233259

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Dec 06 2013

STATUS

approved