A230984 Number of white square subarrays of (n+1) X (3+1) binary arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with upper left element zero.

2, 4, 11, 24, 59, 139, 332, 796, 1903, 4563, 10934, 26209, 62835, 150636, 361156, 865882, 2076002, 4977375, 11933643, 28611925, 68599559, 164473454, 394339672, 945464381, 2266835107, 5434939417, 13030752556, 31242393432, 74906430076

Offset

1,1

Comments

Column 3 of A230989.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 3*a(n-3) - 6*a(n-4) + 2*a(n-5) + 4*a(n-6) - a(n-7) - a(n-8).

Empirical g.f.: x*(2 - 3*x^2 - 4*x^3 + 2*x^4 + 2*x^5 - x^6) / (1 - 2*x - 3*x^2 + 3*x^3 + 6*x^4 - 2*x^5 - 4*x^6 + x^7 + x^8). - Colin Barker, Mar 18 2018

Example

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

Crossrefs

Cf. A230989.

Sequence in context: A362042 A018006 A183510 * A196195 A205500 A342533

Adjacent sequences: A230981 A230982 A230983 * A230985 A230986 A230987

Keyword

nonn

Author

R. H. Hardin, Nov 02 2013

Status

approved