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, 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

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