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A223247
T(n,k)=3-loop graph coloring a rectangular array: number of nXk 0..6 arrays where 0..6 label nodes of a graph with edges 0,1 1,2 2,0 0,3 3,4 4,0 0,5 5,6 6,0 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph
9
7, 18, 18, 60, 102, 60, 168, 642, 642, 168, 528, 4086, 11538, 4086, 528, 1536, 26034, 144582, 144582, 26034, 1536, 4704, 165894, 2663082, 5336844, 2663082, 165894, 4704, 13920, 1057122, 33590454, 198634758, 198634758, 33590454, 1057122, 13920
OFFSET
1,1
COMMENTS
Table starts
......7........18............60...............168...................528
.....18.......102...........642..............4086.................26034
.....60.......642.........11538............144582...............2663082
....168......4086........144582...........5336844.............198634758
....528.....26034.......2663082.........198634758...........22029652542
...1536....165894......33590454........7399451382.........1657797796530
...4704...1057122.....616998282......275682413748.......184125991023066
..13920...6736278....7808992566....10271315554206.....13859263865786022
..42144..42925458..142965076362...382687513971798...1539229991488330446
.125664.273533094.1815370659126.14258133000231516.115867585607831455650
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +6*a(n-2)
k=2: a(n) = 7*a(n-1) -4*a(n-2)
k=3: a(n) = 2*a(n-1) +231*a(n-2) -430*a(n-3) -286*a(n-4) +180*a(n-5)
k=4: a(n) = 40*a(n-1) -80*a(n-2) -869*a(n-3) +1566*a(n-4) +1650*a(n-5) -1796*a(n-6) for n>7
k=5: [order 16]
k=6: [order 24] for n>25
k=7: [order 59]
EXAMPLE
Some solutions for n=3 k=4
..1..0..1..2....0..2..0..1....0..6..0..2....1..0..6..0....0..5..6..0
..0..5..0..1....2..0..4..0....6..0..5..0....0..6..0..4....3..0..5..6
..2..0..1..0....0..4..0..2....0..4..0..3....6..0..5..0....0..2..0..5
CROSSREFS
Sequence in context: A034083 A185455 A103570 * A091832 A374460 A256011
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Mar 18 2013
STATUS
approved