A266935 T(n,k)=Number of nXk binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.
2, 2, 3, 2, 4, 4, 2, 4, 7, 5, 2, 5, 9, 12, 6, 2, 5, 12, 20, 19, 7, 2, 6, 14, 35, 44, 29, 8, 2, 6, 19, 52, 100, 92, 42, 9, 2, 7, 21, 82, 210, 288, 182, 59, 10, 2, 7, 26, 115, 429, 871, 794, 340, 80, 11, 2, 8, 30, 169, 816, 2577, 3566, 2077, 605, 106, 12, 2, 8, 35, 232, 1534, 7185
Offset: 1
Examples
Some solutions for n=4 k=4 ..0..0..0..1....0..0..1..1....0..0..0..1....0..0..0..0....0..0..1..1 ..0..1..1..0....1..1..0..0....1..1..1..0....0..0..0..0....1..1..0..0 ..1..0..0..1....1..1..1..1....1..1..1..1....0..0..0..1....1..1..0..0 ..1..1..1..0....1..1..1..1....1..1..1..1....1..1..1..0....1..1..1..1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..160
Formula
Empirical for column k:
k=1: a(n) = 2*a(n-1) -a(n-2)
k=2: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5)
k=3: [order 11]
k=4: [order 31]
Empirical for row n:
n=1: a(n) = a(n-1)
n=2: a(n) = a(n-1) +a(n-2) -a(n-3)
n=3: a(n) = a(n-1) +a(n-2) -a(n-4) -a(n-5) +a(n-6)
n=4: [order 17]
Comments