A233168 T(n,k)=Number of nXk 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, diagonally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabeled 8-colorings with no clashing color pairs).
1, 1, 1, 3, 1, 3, 11, 8, 8, 11, 48, 64, 96, 64, 48, 236, 512, 1280, 1280, 512, 236, 1248, 4096, 18432, 28672, 18432, 4096, 1248, 6896, 32768, 278528, 720896, 720896, 278528, 32768, 6896, 39168, 262144, 4325376, 19922944, 31457280, 19922944, 4325376
Offset: 1
Examples
Some solutions for n=4 k=4 ..0..1..2..3....0..1..7..1....0..1..7..6....0..1..7..2....0..1..0..6 ..2..4..0..1....2..3..5..3....2..3..5..4....3..2..3..1....2..3..2..4 ..7..6..5..3....7..6..0..6....6..0..1..0....7..1..7..5....0..1..0..6 ..2..4..0..6....3..2..3..5....4..2..3..5....4..5..4..6....3..5..3..2
Links
- R. H. Hardin, Table of n, a(n) for n = 1..544
Crossrefs
Column 2 is A001018(n-2)
Formula
Empirical for column k:
k=1: a(n) = 12*a(n-1) -44*a(n-2) +48*a(n-3) for n>4
k=2: a(n) = 8*a(n-1) for n>2
k=3: a(n) = 24*a(n-1) -128*a(n-2) for n>3
k=4: a(n) = 48*a(n-1) -512*a(n-2) for n>3
k=5: a(n) = 96*a(n-1) -2048*a(n-2) for n>3
k=6: a(n) = 192*a(n-1) -8192*a(n-2) for n>3
k=7: a(n) = 384*a(n-1) -32768*a(n-2) for n>3
Comments