A231338 Number of (n+1) X (2+1) 0..3 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with values 0..3 introduced in row major order.

4, 9, 22, 59, 159, 439, 1236, 3527, 10184, 29679, 87109, 257077, 761860, 2264909, 6749138, 20146867, 60218835, 180167387, 539423380, 1615890811, 4842424660, 14515699655, 43521570985, 130508409225, 391401045892, 1173929246129

Offset

1,1

Links

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

Formula

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

Empirical g.f.: x*(4 - 11*x + x^2 - 5*x^3 + 10*x^4 + 2*x^5 + 3*x^6) / ((1 - x)*(1 - 3*x)*(1 + x + x^2)*(1 - 2*x - x^3)). - Colin Barker, Sep 28 2018

Example

Some solutions for n=6:
..0..0..1....0..0..1....0..1..1....0..0..1....0..0..0....0..0..0....0..0..0
..0..0..1....0..0..1....0..1..1....0..0..1....1..1..1....1..1..0....1..1..1
..1..1..1....1..1..1....0..1..1....1..1..1....1..1..1....1..1..0....1..1..1
..1..2..2....1..1..1....0..1..1....1..0..0....2..2..2....0..0..0....1..1..1
..1..2..2....1..1..1....0..0..0....1..0..0....2..2..2....0..0..0....0..0..0
..1..1..2....1..1..1....1..1..0....1..2..2....2..2..2....2..2..2....0..0..0
..1..1..2....0..0..0....1..1..0....1..2..2....3..3..3....2..2..2....0..0..0

Crossrefs

Column 2 of A231343.

Sequence in context: A122626 A135025 A231213 * A257272 A370021 A070713

Adjacent sequences: A231335 A231336 A231337 * A231339 A231340 A231341

Keyword

nonn

Author

R. H. Hardin, Nov 07 2013

Status

approved