A202973 Number of n X 2 0..1 arrays with every nonzero element less than or equal to at least two horizontal and vertical neighbors.

1, 2, 4, 7, 14, 31, 69, 155, 354, 814, 1875, 4326, 9993, 23095, 53387, 123430, 285394, 659913, 1525942, 3528541, 8159347, 18867623, 43629460, 100888804, 233295503, 539473228, 1247479743, 2884676711, 6670537293, 15424975984, 35668774074

Offset

1,2

Comments

Column 2 of A202979.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 3*a(n-1) - 2*a(n-2) + 2*a(n-3) - 2*a(n-4) - a(n-5).

Empirical g.f.: x*(1 - x - 3*x^3 - x^4) / (1 - 3*x + 2*x^2 - 2*x^3 + 2*x^4 + x^5). - Colin Barker, Feb 19 2018

Example

Some solutions for n=5:
..0..0....0..0....1..1....0..0....1..1....0..0....1..1....1..1....1..1....1..1
..0..0....1..1....1..1....1..1....1..1....0..0....1..1....1..1....1..1....1..1
..0..0....1..1....0..0....1..1....0..0....0..0....1..1....1..1....1..0....0..1
..1..1....0..0....1..1....1..1....0..0....0..0....0..0....1..1....1..1....1..1
..1..1....0..0....1..1....0..0....0..0....0..0....0..0....1..1....1..1....1..1

Crossrefs

Sequence in context: A202842 A364589 A013326 * A074663 A325303 A356781

Adjacent sequences: A202970 A202971 A202972 * A202974 A202975 A202976

Keyword

nonn

Author

R. H. Hardin, Dec 26 2011

Status

approved