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T(n,k)=Generalized Petersen graph (8,2) coloring a rectangular array: number of nXk 0..15 arrays where 0..15 label nodes of a graph with edges 0,1 0,8 8,14 8,10 1,2 1,9 9,15 9,11 2,3 2,10 10,12 3,4 3,11 11,13 4,5 4,12 12,14 5,6 5,13 13,15 6,7 6,14 7,0 7,15 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph
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%I #4 Mar 20 2013 06:29:18

%S 16,48,48,144,256,144,432,1376,1376,432,1296,7424,14112,7424,1296,

%T 3888,40160,147520,147520,40160,3888,11664,217600,1562176,3099264,

%U 1562176,217600,11664,34992,1180256,16693920,67182208,67182208,16693920,1180256

%N T(n,k)=Generalized Petersen graph (8,2) coloring a rectangular array: number of nXk 0..15 arrays where 0..15 label nodes of a graph with edges 0,1 0,8 8,14 8,10 1,2 1,9 9,15 9,11 2,3 2,10 10,12 3,4 3,11 11,13 4,5 4,12 12,14 5,6 5,13 13,15 6,7 6,14 7,0 7,15 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph

%C Table starts

%C .....16........48..........144.............432...............1296

%C .....48.......256.........1376............7424..............40160

%C ....144......1376........14112..........147520............1562176

%C ....432......7424.......147520.........3099264...........67182208

%C ...1296.....40160......1562176........67182208.........3049973040

%C ...3888....217600.....16693920......1485628224.......142702806112

%C ..11664...1180256....179532768.....33277934848......6790055219264

%C ..34992...6405888...1939216640....751557814208....326095786136512

%C .104976..34782688..21008925952..17060996532992..15740601974728144

%C .314928.188912640.228065409888.388541047749184.761894144429277728

%H R. H. Hardin, <a href="/A223440/b223440.txt">Table of n, a(n) for n = 1..220</a>

%F Empirical for column k:

%F k=1: a(n) = 3*a(n-1)

%F k=2: a(n) = 8*a(n-1) -11*a(n-2) -16*a(n-3)

%F k=3: a(n) = 15*a(n-1) -18*a(n-2) -310*a(n-3) +167*a(n-4) +475*a(n-5) -244*a(n-6) -100*a(n-7) +48*a(n-8)

%F k=4: [order 14]

%F k=5: [order 36]

%F k=6: [order 75]

%e Some solutions for n=3 k=4

%e ..7.15..7..0....1..0..7..0...10..8.14.12....8.14.12.10....9..1..9.11

%e ..6..7..6..7....2..1..0..7...12.10.12.14...14.12.10..8....1..9.11..9

%e ..7.15..7.15...10..2..1..0...14..8.14..8....8.14.12.14....9..1..9..1

%Y Column 1 is A188825(n+1)

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Mar 20 2013