A230983 Number of white square subarrays of (n+1) X (2+1) binary arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with upper left element zero.

1, 1, 4, 5, 15, 20, 57, 77, 218, 295, 835, 1130, 3199, 4329, 12256, 16585, 46955, 63540, 179893, 243433, 689202, 932635, 2640455, 3573090, 10116051, 13689141, 38756384, 52445525, 148482575, 200928100, 568863057, 769791157, 2179415178, 2949206335

Offset

1,3

Links

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

Formula

Empirical: a(n) = 5*a(n-2) - 5*a(n-4) + 2*a(n-6).

Empirical g.f.: x*(1 + x - x^2) / (1 - 5*x^2 + 5*x^4 - 2*x^6). - Colin Barker, Sep 25 2018

Example

Some solutions for n=6:
..0..x..0....0..x..0....0..x..0....0..x..0....0..x..0....0..x..0....0..x..0
..x..1..x....x..1..x....x..1..x....x..1..x....x..1..x....x..1..x....x..1..x
..0..x..0....0..x..0....0..x..0....1..x..0....0..x..1....1..x..1....0..x..1
..x..0..x....x..0..x....x..1..x....x..0..x....x..0..x....x..0..x....x..0..x
..1..x..1....1..x..1....1..x..1....1..x..0....1..x..0....1..x..0....1..x..1
..x..1..x....x..0..x....x..0..x....x..1..x....x..1..x....x..1..x....x..0..x
..0..x..0....1..x..1....1..x..1....0..x..0....0..x..0....0..x..0....1..x..1

Crossrefs

Column 2 of A230989.

Sequence in context: A066516 A047184 A002509 * A100234 A007390 A037955

Adjacent sequences: A230980 A230981 A230982 * A230984 A230985 A230986

Keyword

nonn

Author

R. H. Hardin, Nov 02 2013

Status

approved