A231295 Number of (n+1) X (1+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with values 0..2 introduced in row major order.

1, 2, 4, 12, 32, 92, 264, 756, 2176, 6252, 17976, 51684, 148592, 427228, 1228328, 3531604, 10153824, 29193548, 83935256, 241324740, 693839952, 1994879932, 5735538696, 16490418228, 47412092736, 136315920428, 391925964280

Offset

1,2

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) - 4*a(n-4).

Empirical g.f.: x*(1 + x)^2*(1 - 2*x) / ((1 - x)*(1 - x - 4*x^2 - 4*x^3)). - Colin Barker, Sep 28 2018

Example

Some solutions for n=4:
..0..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..1....0..1....0..0....0..0....0..0....0..0....0..0
..0..1....1..1....1..1....1..1....1..1....0..0....1..1....1..1....0..0....0..0
..1..1....1..1....0..0....2..2....1..1....0..1....1..2....1..0....1..1....0..0
..1..1....1..1....0..0....2..2....1..1....1..1....2..2....0..0....1..1....0..0

Crossrefs

Column 1 of A231302.

Sequence in context: A152035 A026151 A025178 * A087211 A161177 A039721

Adjacent sequences: A231292 A231293 A231294 * A231296 A231297 A231298

Keyword

nonn

Author

R. H. Hardin, Nov 07 2013

Status

approved