|
| |
|
|
A223423
|
|
T(n,k)=3-level binary fanout graph coloring a rectangular array: number of nXk 0..6 arrays where 0..6 label nodes of a graph with edges 0,1 1,3 1,4 0,2 2,5 2,6 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph
|
|
8
|
|
|
|
7, 12, 12, 26, 40, 26, 48, 136, 136, 48, 104, 464, 868, 464, 104, 192, 1584, 4720, 4720, 1584, 192, 416, 5408, 29912, 47872, 29912, 5408, 416, 768, 18464, 163168, 486016, 486016, 163168, 18464, 768, 1664, 63040, 1033328, 4934272, 9210784, 4934272
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
Table starts
....7.....12........26..........48............104..............192
...12.....40.......136.........464...........1584.............5408
...26....136.......868........4720..........29912...........163168
...48....464......4720.......47872.........486016..........4934272
..104...1584.....29912......486016........9210784........150006016
..192...5408....163168.....4934272......150006016.......4565849088
..416..18464...1033328....50097024.....2844612736.....139114196992
..768..63040...5638336...508632832....46345527296....4240305623040
.1664.215232..35704800..5164146176...878977950208..129279082045440
.3072.734848.194827648.52431620096.14321836797952.3941937218551808
|
|
|
LINKS
|
|
|
|
FORMULA
|
Empirical for column k:
k=1: a(n) = 4*a(n-2) for n>3
k=2: a(n) = 4*a(n-1) -2*a(n-2)
k=3: a(n) = 38*a(n-2) -120*a(n-4) +32*a(n-6)
k=4: a(n) = 14*a(n-1) -36*a(n-2) -40*a(n-3) +88*a(n-4) +32*a(n-5) -32*a(n-6)
k=5: a(n) = 392*a(n-2) -26768*a(n-4) +353408*a(n-6) -1274624*a(n-8) +1441792*a(n-10) -307200*a(n-12) for n>13
k=6: [order 18]
k=7: [order 36]
|
|
|
EXAMPLE
|
Some solutions for n=3 k=4
..5..2..6..2....5..2..0..1....1..3..1..0....1..0..1..4....0..2..6..2
..2..0..2..6....2..6..2..0....3..1..4..1....4..1..4..1....1..0..2..0
..0..1..0..2....6..2..0..1....1..4..1..0....1..3..1..4....4..1..0..2
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
