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

R. H. Hardin, Table of n, a(n) for n = 1..238

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 A256011 A272972

Adjacent sequences:  A223244 A223245 A223246 * A223248 A223249 A223250

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Mar 18 2013

STATUS

approved

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Last modified May 26 09:04 EDT 2022. Contains 354077 sequences. (Running on oeis4.)