A262759 T(n,k) = Number of (n+2) X (k+2) 0..1 arrays with each row divisible by 5 and each column divisible by 7, read as a binary number with top and left being the most significant bits.
2, 4, 3, 7, 9, 5, 13, 17, 25, 10, 26, 37, 49, 100, 19, 52, 107, 129, 319, 361, 37, 103, 321, 709, 1645, 1345, 1369, 74, 205, 865, 4953, 16450, 8605, 6193, 5476, 147, 410, 2449, 16705, 243220, 135595, 52993, 39751, 21609, 293, 820, 7299, 73345, 1614175
Offset: 1
Examples
Some solutions for n=4, k=4 ..1..0..0..0..1..1....1..1..1..1..0..0....1..0..0..0..1..1....1..1..1..1..0..0 ..1..0..1..0..0..0....1..1..1..1..0..0....1..0..1..1..0..1....1..1..0..0..1..0 ..1..0..0..0..1..1....1..1..1..1..0..0....1..0..1..0..0..0....1..0..1..1..0..1 ..1..1..1..1..0..0....0..1..1..0..0..1....1..1..1..1..0..0....1..0..0..0..1..1 ..1..1..0..1..1..1....0..1..1..0..0..1....1..1..0..0..1..0....1..0..1..1..0..1 ..1..1..1..1..0..0....0..1..1..0..0..1....1..1..0..1..1..1....1..1..0..0..1..0
Links
- R. H. Hardin, Table of n, a(n) for n = 1..84
Formula
Empirical for column k:
k=1: a(n) = 2*a(n-1) +a(n-3) -2*a(n-4)
k=2: a(n) = 4*a(n-1) +9*a(n-3) -36*a(n-4) -8*a(n-6) +32*a(n-7)
Empirical for row n:
n=1: a(n) = 3*a(n-1) -3*a(n-2) +3*a(n-3) -2*a(n-4)
n=2: [order 8]
n=3: [order 17]
n=4: [order 16]
Comments