A263873 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits, and rows and columns lexicographically nondecreasing.
2, 2, 2, 3, 2, 3, 3, 3, 3, 3, 4, 3, 7, 3, 4, 4, 4, 7, 7, 4, 4, 5, 4, 14, 7, 14, 4, 5, 5, 5, 14, 16, 16, 14, 5, 5, 6, 5, 25, 17, 61, 17, 25, 5, 6, 6, 6, 25, 41, 93, 93, 41, 25, 6, 6, 7, 6, 41, 48, 494, 379, 494, 48, 41, 6, 7, 7, 7, 41, 113, 975, 2909, 2909, 975, 113, 41, 7, 7, 8, 7, 63, 141
Offset: 1
Examples
Some solutions for n=4 k=4 ..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0 ..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..1..1..1..1 ..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..1..1..1..1 ..0..0..0..1..1....0..1..1..1..1....0..0..0..0..0....0..1..1..1..1 ..0..0..0..1..1....0..1..1..1..1....0..0..0..0..0....0..1..1..1..1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..144
Formula
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2) -a(n-3)
k=2: a(n) = a(n-1) +a(n-2) -a(n-3)
k=3: a(n) = a(n-1) +3*a(n-2) -3*a(n-3) -3*a(n-4) +3*a(n-5) +a(n-6) -a(n-7)
k=4: [order 14]
k=5: [order 37]
k=6: [order 79]
Comments