A241073 Number of n X 2 0..2 arrays with no element equal to exactly one horizontal or vertical neighbor, with new values 0..2 introduced in row major order.

1, 4, 12, 39, 131, 444, 1516, 5195, 17847, 61424, 211672, 730119, 2520091, 8702628, 30063396, 103881123, 359017439, 1240945016, 4289745552, 14829991071, 51271047939, 177263517036, 612883590684, 2119068084731, 7326858673287

Offset

1,2

Links

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

Formula

Empirical: a(n) = 6*a(n-1) - 8*a(n-2) - 4*a(n-3) + a(n-4) + 14*a(n-5) - 8*a(n-6) for n>7.

Empirical g.f.: x*(1 + x)*(1 - 3*x - x^2 + 4*x^3 + 4*x^4 - 4*x^5) / ((1 - x)*(1 - 5*x + 3*x^2 + 7*x^3 + 6*x^4 - 8*x^5)). - Colin Barker, Oct 29 2018

Example

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

Crossrefs

Column 2 of A241078.

Sequence in context: A308446 A334458 A122920 * A149328 A149329 A149330

Adjacent sequences: A241070 A241071 A241072 * A241074 A241075 A241076

Keyword

nonn

Author

R. H. Hardin, Apr 15 2014

Status

approved