A223305 T(n,k)=4X4X4 triangular graph coloring a rectangular array: number of nXk 0..9 arrays where 0..9 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 3,6 3,7 4,7 6,7 4,8 5,8 7,8 5,9 8,9 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

10, 36, 36, 144, 324, 144, 576, 3132, 3132, 576, 2304, 30564, 76788, 30564, 2304, 9216, 298620, 1882500, 1882500, 298620, 9216, 36864, 2918052, 46589268, 118001928, 46589268, 2918052, 36864, 147456, 28515132, 1148040516, 7442199324, 7442199324

Offset: 1

Author

R. H. Hardin Mar 19 2013

Keywords

• nonn
• tabl

Comments

Table starts

.....10........36..........144..............576................2304

.....36.......324.........3132............30564..............298620

....144......3132........76788..........1882500............46589268

....576.....30564......1882500........118001928..........7442199324

...2304....298620.....46589268.......7442199324.......1208825525124

...9216...2918052...1148040516.....470062209228.....195984333263964

..36864..28515132..28402185108...29706324866280...31982581839418764

.147456.278649828.700525554180.1877636655597516.5198236290762699924

Examples

			Some solutions for n=3 k=4
..5..2..4..2....5..2..5..4....0..2..0..2....0..1..4..7....0..2..4..7
..2..5..2..0....2..5..4..8....2..1..2..5....2..0..2..4....2..4..1..4
..0..2..4..1....5..4..2..4....4..2..5..8....1..2..5..8....4..3..4..8
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..161

Crossrefs

Column 1 is A002063(n-1) for n>1

Formula

Empirical for column k:

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

k=2: a(n) = 11*a(n-1) -12*a(n-2)

k=3: [order 11] for n>12

k=4: [order 25] for n>26