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

1,1

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A188825(n+1)

Sequence in context: A083307 A235765 A235548 * A223402 A260985 A322448

Adjacent sequences: A223437 A223438 A223439 * A223441 A223442 A223443

Keyword

nonn,tabl

Author

R. H. Hardin Mar 20 2013

Status

approved