A240778 Number of n X 3 0..1 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..1 introduced in row major order.

1, 4, 20, 97, 459, 2187, 10442, 49861, 238068, 1136678, 5427201, 25912833, 123723975, 590735140, 2820536641, 13466994652, 64299801122, 307007207679, 1465843189533, 6998846289463, 33416841401200, 159552766705917

Offset: 1

Author

R. H. Hardin, Apr 12 2014

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Column 3 of A240783.

Formula

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

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