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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 8
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Mar 20 2013
STATUS
approved

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Last modified February 20 21:52 EST 2024. Contains 370219 sequences. (Running on oeis4.)