A232335 T(n,k)=Number of nXk 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or antidiagonally, with no adjacent elements equal.
1, 2, 1, 4, 6, 1, 6, 18, 16, 1, 10, 32, 74, 42, 1, 16, 82, 154, 308, 110, 1, 26, 162, 628, 734, 1282, 288, 1, 42, 388, 1470, 4906, 3472, 5338, 754, 1, 68, 806, 5530, 13170, 38986, 16338, 22228, 1974, 1, 110, 1858, 13906, 82526, 117690, 312276, 76630, 92562, 5168
Offset: 1
Examples
Some solutions for n=5 k=4 ..2..1..0..1....2..1..2..1....2..1..0..2....1..2..0..2....2..1..0..1 ..0..1..2..0....0..1..2..0....0..2..1..0....0..1..0..1....2..1..2..1 ..2..0..1..0....2..0..1..0....1..2..1..0....2..1..2..1....2..1..0..2 ..1..2..1..2....1..2..1..2....1..2..1..0....0..1..0..2....0..2..1..2 ..1..0..1..0....1..2..1..0....1..0..2..1....2..1..0..2....1..0..1..2
Links
- R. H. Hardin, Table of n, a(n) for n = 1..448
Formula
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 3*a(n-1) -a(n-2)
k=3: a(n) = 5*a(n-1) -3*a(n-2) -2*a(n-3)
k=4: a(n) = 7*a(n-1) -9*a(n-2) -8*a(n-3) -4*a(n-4)
k=5: a(n) = 11*a(n-1) -21*a(n-2) -20*a(n-3) -12*a(n-4) for n>5
k=6: [order 7] for n>9
k=7: [order 16] for n>18
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2) for n>3
n=2: a(n) = a(n-1) +3*a(n-2) -a(n-3) +a(n-4) -a(n-5) for n>6
n=3: [order 8] for n>12
n=4: [order 21] for n>24
n=5: [order 36] for n>42
n=6: [order 80] for n>87
Comments