A228506 T(n,k)=Number of nXk binary arrays with top left value 1 and no two ones adjacent horizontally, vertically, diagonally or antidiagonally.

1, 1, 1, 2, 1, 2, 3, 3, 3, 3, 5, 5, 12, 5, 5, 8, 11, 29, 29, 11, 8, 13, 21, 88, 87, 88, 21, 13, 21, 43, 239, 358, 358, 239, 43, 21, 34, 85, 684, 1252, 2002, 1252, 684, 85, 34, 55, 171, 1909, 4749, 9528, 9528, 4749, 1909, 171, 55, 89, 341, 5392, 17285, 49101, 59839, 49101

Offset: 1

Author

R. H. Hardin Aug 23 2013

Keywords

• nonn
• tabl

Comments

Table starts

..1...1....2.....3.......5........8........13.........21..........34

..1...1....3.....5......11.......21........43.........85.........171

..2...3...12....29......88......239.......684.......1909........5392

..3...5...29....87.....358.....1252......4749......17285.......64235

..5..11...88...358....2002.....9528.....49101.....243118.....1228036

..8..21..239..1252....9528....59839....413786....2724191....18387032

.13..43..684..4749...49101...413786...3862849...34229311...311423874

.21..85.1909.17285..243118..2724191..34229311..405580157..4951454523

.34.171.5392.64235.1228036.18387032.311423874.4951454523.81304395949

Examples

			Some solutions for n=4 k=4
..1..0..0..0....1..0..0..0....1..0..0..1....1..0..0..0....1..0..0..1
..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..0..0..0....0..0..0..0....0..0..0..1....1..0..0..0
..1..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..1..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1740

Crossrefs

Column 1 is A000045

Column 2 is A001045

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2)

k=2: a(n) = a(n-1) +2*a(n-2)

k=3: a(n) = 2*a(n-1) +3*a(n-2) -2*a(n-3)

k=4: a(n) = 2*a(n-1) +7*a(n-2) -2*a(n-3) -3*a(n-4)

k=5: a(n) = 2*a(n-1) +16*a(n-2) +a(n-3) -27*a(n-4) +a(n-5) +4*a(n-6)

k=6: [order 8]

k=7: [order 14]