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

1,4

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A000045

Column 2 is A001045

Sequence in context: A003986 A343836 A123603 * A228285 A020908 A240873

Adjacent sequences: A228503 A228504 A228505 * A228507 A228508 A228509

Keyword

nonn,tabl

Author

R. H. Hardin Aug 23 2013

Status

approved