A223440 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.

16, 48, 48, 144, 256, 144, 432, 1376, 1376, 432, 1296, 7424, 14112, 7424, 1296, 3888, 40160, 147520, 147520, 40160, 3888, 11664, 217600, 1562176, 3099264, 1562176, 217600, 11664, 34992, 1180256, 16693920, 67182208, 67182208, 16693920, 1180256

Offset: 1

Author

R. H. Hardin Mar 20 2013

Keywords

• nonn
• tabl

Comments

Table starts

.....16........48..........144.............432...............1296

.....48.......256.........1376............7424..............40160

....144......1376........14112..........147520............1562176

....432......7424.......147520.........3099264...........67182208

...1296.....40160......1562176........67182208.........3049973040

...3888....217600.....16693920......1485628224.......142702806112

..11664...1180256....179532768.....33277934848......6790055219264

..34992...6405888...1939216640....751557814208....326095786136512

.104976..34782688..21008925952..17060996532992..15740601974728144

.314928.188912640.228065409888.388541047749184.761894144429277728

Examples

			Some solutions for n=3 k=4
..7.15..7..0....1..0..7..0...10..8.14.12....8.14.12.10....9..1..9.11
..6..7..6..7....2..1..0..7...12.10.12.14...14.12.10..8....1..9.11..9
..7.15..7.15...10..2..1..0...14..8.14..8....8.14.12.14....9..1..9..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..220

Crossrefs

Column 1 is A188825(n+1)

Formula

Empirical for column k:

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

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

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)

k=4: [order 14]

k=5: [order 36]

k=6: [order 75]