login
A223692
T(n,k)=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 antidiagonal neighbor moves along an edge of this graph
13
16, 48, 256, 144, 432, 4096, 432, 2304, 3888, 65536, 1296, 12384, 37008, 34992, 1048576, 3888, 66816, 363600, 595584, 314928, 16777216, 11664, 361440, 3788640, 10817856, 9594000, 2834352, 268435456, 34992, 1958400, 40075632, 223096320
OFFSET
1,1
COMMENTS
Table starts
............16..........48............144..............432.................1296
...........256.........432...........2304............12384................66816
..........4096........3888..........37008...........363600..............3788640
.........65536.......34992.........595584.........10817856............223096320
.......1048576......314928........9594000........324280368..........13402129824
......16777216.....2834352......154616832.......9762152544.........814399853760
.....268435456....25509168.....2492365968.....294583794768.......49817845241568
....4294967296...229582512....40180445568....8901308553408.....3059068970173824
...68719476736..2066242608...647800215696..269168305340592...188252023352797728
.1099511627776.18596183472.10444288589568.8142829402619232.11599193857488796224
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 16*a(n-1)
k=2: a(n) = 9*a(n-1)
k=3: a(n) = 24*a(n-1) -127*a(n-2)
k=4: a(n) = 59*a(n-1) -1103*a(n-2) +7621*a(n-3) -16900*a(n-4)
k=5: [order 7] for n>8
k=6: [order 17]) for n>18
k=7: [order 37] for n>39
Empirical for row n:
n=1: a(n) = 3*a(n-1)
n=2: a(n) = 8*a(n-1) -11*a(n-2) -16*a(n-3) for n>4
n=3: a(n) = [order 10]) for n>12
n=4: a(n) = [order 24] for n>27
n=5: a(n) = [order 56] for n>61
EXAMPLE
Some solutions for n=3 k=4
..2..1..9..1....6..5..4..5....6.14..6.14....4..3..2.10....2..3..4..3
..2..1..9.11....4..5..6.14...12.14..8.14....2.10..2.10....4..3.11.13
..9.11..9.15....6..7..6.14....8..0..8..0....8.10..8.10...11.13.11..9
CROSSREFS
Column 1 is A001025
Column 2 is 48*9^(n-1)
Row 1 is A188825(n+1)
Sequence in context: A223395 A202329 A223599 * A165115 A165117 A226966
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Mar 25 2013
STATUS
approved