A223247 - OEIS

%I #4 Mar 18 2013 20:55:32

%S 7,18,18,60,102,60,168,642,642,168,528,4086,11538,4086,528,1536,26034,

%T 144582,144582,26034,1536,4704,165894,2663082,5336844,2663082,165894,

%U 4704,13920,1057122,33590454,198634758,198634758,33590454,1057122,13920

%N 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

%C Table starts

%C ......7........18............60...............168...................528

%C .....18.......102...........642..............4086.................26034

%C .....60.......642.........11538............144582...............2663082

%C ....168......4086........144582...........5336844.............198634758

%C ....528.....26034.......2663082.........198634758...........22029652542

%C ...1536....165894......33590454........7399451382.........1657797796530

%C ...4704...1057122.....616998282......275682413748.......184125991023066

%C ..13920...6736278....7808992566....10271315554206.....13859263865786022

%C ..42144..42925458..142965076362...382687513971798...1539229991488330446

%C .125664.273533094.1815370659126.14258133000231516.115867585607831455650

%H R. H. Hardin, <a href="/A223247/b223247.txt">Table of n, a(n) for n = 1..238</a>

%F Empirical for column k:

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

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

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

%F 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

%F k=5: [order 16]

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

%F k=7: [order 59]

%e Some solutions for n=3 k=4

%e ..1..0..1..2....0..2..0..1....0..6..0..2....1..0..6..0....0..5..6..0

%e ..0..5..0..1....2..0..4..0....6..0..5..0....0..6..0..4....3..0..5..6

%e ..2..0..1..0....0..4..0..2....0..4..0..3....6..0..5..0....0..2..0..5

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Mar 18 2013