A223247 T(n,k)=3-loop graph coloring a rectangular array: number of nXk 0..6 arrays where 0..6 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 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph

7, 18, 18, 60, 102, 60, 168, 642, 642, 168, 528, 4086, 11538, 4086, 528, 1536, 26034, 144582, 144582, 26034, 1536, 4704, 165894, 2663082, 5336844, 2663082, 165894, 4704, 13920, 1057122, 33590454, 198634758, 198634758, 33590454, 1057122, 13920

Offset

1,1

Comments

Table starts

......7........18............60...............168...................528

.....18.......102...........642..............4086.................26034

.....60.......642.........11538............144582...............2663082

....168......4086........144582...........5336844.............198634758

....528.....26034.......2663082.........198634758...........22029652542

...1536....165894......33590454........7399451382.........1657797796530

...4704...1057122.....616998282......275682413748.......184125991023066

..13920...6736278....7808992566....10271315554206.....13859263865786022

..42144..42925458..142965076362...382687513971798...1539229991488330446

.125664.273533094.1815370659126.14258133000231516.115867585607831455650

Links

R. H. Hardin, Table of n, a(n) for n = 1..238

Formula

Empirical for column k:

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

k=2: a(n) = 7*a(n-1) -4*a(n-2)

k=3: a(n) = 2*a(n-1) +231*a(n-2) -430*a(n-3) -286*a(n-4) +180*a(n-5)

k=4: a(n) = 40*a(n-1) -80*a(n-2) -869*a(n-3) +1566*a(n-4) +1650*a(n-5) -1796*a(n-6) for n>7

k=5: [order 16]

k=6: [order 24] for n>25

k=7: [order 59]

Example

Some solutions for n=3 k=4
..1..0..1..2....0..2..0..1....0..6..0..2....1..0..6..0....0..5..6..0
..0..5..0..1....2..0..4..0....6..0..5..0....0..6..0..4....3..0..5..6
..2..0..1..0....0..4..0..2....0..4..0..3....6..0..5..0....0..2..0..5

Crossrefs

Sequence in context: A034083 A185455 A103570 * A091832 A374460 A256011

Adjacent sequences: A223244 A223245 A223246 * A223248 A223249 A223250

Keyword

nonn,tabl

Author

R. H. Hardin Mar 18 2013

Status

approved