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A223297 T(n,k)=4-loop graph coloring a rectangular array: number of nXk 0..8 arrays where 0..8 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 0,7 7,8 8,0 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph 9
9, 24, 24, 96, 168, 96, 288, 1368, 1368, 288, 1056, 11304, 42168, 11304, 1056, 3360, 93528, 709320, 709320, 93528, 3360, 11808, 773928, 22346136, 46008720, 22346136, 773928, 11808, 38688, 6404184, 377262504, 2997483624, 2997483624, 377262504 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

......9.........24..............96.................288.....................1056

.....24........168............1368...............11304....................93528

.....96.......1368...........42168..............709320.................22346136

....288......11304..........709320............46008720...............2997483624

...1056......93528........22346136..........2997483624.............757664837832

...3360.....773928.......377262504........195340203144..........101979342907800

..11808....6404184.....11864385048......12730353920784........25787363600621016

..38688...52994088....200704309992.....829641130218216......3471044597151840072

.133152..438521688...6299392974744...54067983864017544....877705282143571802568

.442656.3628730664.106774437227112.3523628257995013776.118143428663004983310744

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..199

FORMULA

Empirical for column k:

k=1: a(n) = a(n-1) +8*a(n-2)

k=2: a(n) = 9*a(n-1) -6*a(n-2)

k=3: a(n) = 2*a(n-1) +531*a(n-2) -1022*a(n-3) -750*a(n-4) +448*a(n-5)

k=4: a(n) = 68*a(n-1) -156*a(n-2) -1911*a(n-3) +3816*a(n-4) +3960*a(n-5) -4572*a(n-6) for n>7

k=5: [order 16]

k=6: [order 24] for n>25

EXAMPLE

Some solutions for n=3 k=4

..0..1..0..5....0..3..0..7....0..3..0..3....0..3..0..6....1..0..8..0

..2..0..1..0....3..0..6..0....2..0..8..0....2..0..2..0....0..3..0..5

..0..6..0..1....0..2..0..6....0..1..0..1....0..8..0..1....4..0..4..0

CROSSREFS

Sequence in context: A347559 A161431 A223379 * A317493 A102217 A124065

Adjacent sequences:  A223294 A223295 A223296 * A223298 A223299 A223300

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Mar 19 2013

STATUS

approved

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Last modified October 4 04:26 EDT 2022. Contains 357237 sequences. (Running on oeis4.)