A302010 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 3 horizontally or antidiagonally adjacent elements, with upper left element zero.
1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 240, 128, 16, 32, 512, 1808, 1808, 512, 32, 64, 2048, 13616, 25808, 13616, 2048, 64, 128, 8192, 102544, 369040, 368144, 102544, 8192, 128, 256, 32768, 772272, 5276816, 9989376, 5251712, 772272, 32768, 256, 512, 131072
Offset: 1
Examples
Some solutions for n=5 k=4 ..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..1. .0..0..0..0 ..1..0..0..1. .1..0..1..0. .0..1..0..1. .1..1..0..0. .0..0..1..0 ..0..1..0..0. .0..0..1..1. .1..1..1..0. .0..0..1..0. .0..0..0..1 ..1..1..1..1. .1..1..0..0. .0..0..0..0. .0..1..0..0. .1..1..0..1 ..0..1..0..1. .0..0..1..0. .0..1..0..0. .1..1..1..0. .0..0..0..0
Links
- R. H. Hardin, Table of n, a(n) for n = 1..479
Crossrefs
Formula
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1)
k=3: a(n) = 7*a(n-1) +4*a(n-2)
k=4: a(n) = 13*a(n-1) +18*a(n-2) +a(n-3) -4*a(n-4)
k=5: a(n) = 24*a(n-1) +82*a(n-2) +34*a(n-3) -90*a(n-4) -40*a(n-5) +37*a(n-6)
k=6: [order 10] for n>12
k=7: [order 17] for n>19
Empirical for row n:
n=1: a(n) = 2*a(n-1)
n=2: a(n) = 4*a(n-1)
n=3: a(n) = 7*a(n-1) +4*a(n-2)
n=4: a(n) = 13*a(n-1) +20*a(n-2) -16*a(n-3) -64*a(n-4) for n>6
n=5: [order 12] for n>15
n=6: [order 32] for n>36
n=7: [order 78] for n>83
Comments