A230675 T(n,k)=Number of nXk 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value 2-x(i,j).
0, 3, 0, 3, 15, 0, 9, 87, 81, 0, 15, 513, 1173, 423, 0, 33, 3387, 18915, 17271, 2247, 0, 63, 21933, 340563, 730503, 251595, 11925, 0, 129, 141411, 6081561, 37034355, 28368687, 3669765, 63291, 0, 255, 913245, 108108231, 1844154933, 4022141121, 1100265795
Offset: 1
Examples
Some solutions for n=3 k=4 ..0..2..0..2....2..0..0..2....2..0..1..2....0..0..0..2....1..1..1..1 ..0..0..1..1....0..1..0..2....1..1..0..1....2..2..0..1....1..2..1..2 ..2..2..0..1....1..2..1..2....1..1..1..2....2..0..1..2....2..0..0..2
Links
- R. H. Hardin, Table of n, a(n) for n = 1..126
Formula
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 5*a(n-1) +2*a(n-2) -a(n-3) -5*a(n-4)
k=3: a(n) = 14*a(n-1) +9*a(n-2) -9*a(n-3) +30*a(n-4) -19*a(n-5)
k=4: [order 32]
k=5: [order 80]
Empirical for row n:
n=1: a(n) = a(n-1) +2*a(n-2)
n=2: a(n) = 5*a(n-1) +6*a(n-2) +20*a(n-3) +12*a(n-4) +8*a(n-5)
n=3: [order 15] for n>16
n=4: [order 64] for n>65
Comments