A223218 T(n,k)=3X3X3 triangular graph coloring a rectangular array: number of nXk 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,2 1,2 1,3 1,4 2,4 3,4 2,5 4,5 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph

6, 18, 18, 60, 126, 60, 192, 918, 918, 192, 624, 6642, 15498, 6642, 624, 2016, 48114, 254694, 254694, 48114, 2016, 6528, 348462, 4232586, 9640008, 4232586, 348462, 6528, 21120, 2523798, 70014654, 367156350, 367156350, 70014654, 2523798, 21120

Offset

1,1

Comments

Table starts

......6........18............60...............192...................624

.....18.......126...........918..............6642.................48114

.....60.......918.........15498............254694...............4232586

....192......6642........254694...........9640008.............367156350

....624.....48114.......4232586.........367156350...........32213930742

...2016....348462......70014654.......13964418774.........2819203560630

...6528...2523798....1160465118......531419938920.......247143798101322

..21120..18278946...19217863458....20220127602030.....21653415762483246

..68352.132387858..318374151654...769404277676466...1897735773641654046

.221184.958837662.5273531868834.29276398278326448.166300121937966179310

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1) +4*a(n-2)

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

k=3: [order 8]

k=4: [order 15]

k=5: [order 45]

k=6: [order 77]

Example

Some solutions for n=3 k=4
..0..1..0..1....0..1..2..5....4..3..1..2....0..2..1..4....0..1..4..1
..1..4..1..4....1..2..5..4....3..4..2..1....1..4..2..1....1..0..1..4
..2..1..2..5....4..1..4..5....4..3..1..4....0..2..1..2....4..2..4..5

Crossrefs

Sequence in context: A074390 A255617 A253771 * A077630 A361730 A371989

Adjacent sequences: A223215 A223216 A223217 * A223219 A223220 A223221

Keyword

nonn,tabl

Author

R. H. Hardin Mar 18 2013

Status

approved