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

1,1

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

Links

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

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

Example

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

Crossrefs

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

Sequence in context: A126249 A125550 A343155 * A176575 A073613 A346386

Adjacent sequences: A223302 A223303 A223304 * A223306 A223307 A223308

Keyword

nonn,tabl

Author

R. H. Hardin Mar 19 2013

Status

approved