|
| |
|
|
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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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: A291857 A300672 A052407 * A185350 A279910 A105039
Adjacent sequences: A233171 A233172 A233173 * A233175 A233176 A233177
|
|
|
KEYWORD
|
nonn,tabl
|
|
|
AUTHOR
|
R. H. Hardin, Dec 05 2013
|
|
|
STATUS
|
approved
|
| |
|
|
