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

Author

R. H. Hardin Mar 18 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

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]