A302212 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
1, 1, 2, 1, 2, 4, 1, 11, 2, 8, 1, 13, 16, 3, 16, 1, 34, 5, 47, 6, 32, 1, 65, 32, 7, 147, 10, 64, 1, 123, 22, 111, 18, 386, 21, 128, 1, 266, 72, 80, 448, 55, 1065, 42, 256, 1, 499, 101, 424, 281, 1725, 172, 3063, 86, 512, 1, 1037, 216, 1157, 1868, 1395, 6423, 575, 8624, 179
Offset: 1
Examples
Some solutions for n=5 k=4 ..0..1..0..0. .0..1..0..0. .0..0..1..0. .0..1..0..0. .0..0..1..1 ..0..1..0..0. .0..1..0..0. .0..0..1..0. .0..1..0..0. .0..0..1..1 ..1..1..1..0. .1..1..1..1. .1..1..1..1. .0..1..0..1. .0..1..1..0 ..0..1..0..0. .0..0..1..0. .0..1..0..0. .0..1..0..0. .0..0..1..1 ..0..1..0..0. .0..0..1..0. .0..1..0..0. .0..1..0..0. .0..0..1..1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..240
Formula
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
k=3: [order 9]
k=4: [order 28] for n>32
k=5: [order 37] for n>41
Empirical for row n:
n=1: a(n) = a(n-1)
n=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5
n=3: [order 19] for n>20
n=4: [order 61] for n>62
Comments