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.
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, 324280368, 154616832, 25509168, 4294967296
Offset: 1
Examples
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, ...
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
Links
- R. H. Hardin, Table of n, a(n) for n = 1..218
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