A223599 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, diagonal or antidiagonal neighbor moves along an edge of this graph.
16, 48, 256, 144, 256, 4096, 432, 1504, 1376, 65536, 1296, 6736, 16192, 7424, 1048576, 3888, 32768, 122608, 176224, 40160, 16777216, 11664, 156592, 1124064, 2372080, 1931968, 217600, 268435456, 34992, 755200, 9902320, 43725920, 47659632
Offset: 1
Examples
Some solutions for n=3 k=4 .14..6..5.13...13.15..9.15...12..4.12.10....6..5.13.15....8.14..8.10 ..7..6..5..6...13.15..9..1...12..4.12..4....6..5.13..5....8.14..8.14 ..5..6.14..6....9.15..9.11....5..4.12.14...13..5..6..5....6.14..6.14
Links
- R. H. Hardin, Table of n, a(n) for n = 1..161
Formula
Empirical for column k:
k=1: a(n) = 16*a(n-1)
k=2: a(n) = 8*a(n-1) -11*a(n-2) -16*a(n-3)
k=3: a(n) = 23*a(n-1) -153*a(n-2) +217*a(n-3) +258*a(n-4) -456*a(n-5) -104*a(n-6) +192*a(n-7)
k=4: [order 9]
k=5: [order 29]
k=6: [order 55]
Empirical for row n:
n=1: a(n) = 3*a(n-1)
n=2: a(n) = 6*a(n-1) +3*a(n-2) -42*a(n-3) -8*a(n-4) +48*a(n-5) for n>6
n=3: [order 11] for n>12
n=4: [order 28] for n>29
n=5: [order 74] for n>75
Comments