A233020 Number of n X 2 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, vertically, diagonally or antidiagonally, and top left element zero.

3, 15, 81, 435, 2337, 12555, 67449, 362355, 1946673, 10458075, 56183721, 301834755, 1621541217, 8711375595, 46799960409, 251422553235, 1350712686993, 7256408541435, 38983468081161, 209430157488675, 1125117723605697

Offset: 1

Author

R. H. Hardin, Dec 03 2013

Keywords

• nonn

Examples

			Some solutions for n=5:
..0..2....0..0....0..0....0..1....0..0....0..0....0..1....0..2....0..0....0..0
..2..2....1..1....2..2....1..1....1..1....0..2....0..1....2..0....1..1....0..0
..3..2....1..1....2..3....0..0....0..0....2..2....0..1....2..0....1..1....1..1
..3..2....1..3....3..3....2..2....1..1....2..3....0..1....0..2....3..3....3..1
..2..3....3..3....3..2....0..0....3..1....2..3....0..1....0..2....2..3....3..1
		

Links

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

Crossrefs

Column 2 of A233026.

Formula

Empirical: a(n) = 5*a(n-1) + 2*a(n-2).

Conjectures from Colin Barker, Oct 06 2018: (Start)

G.f.: 3*x / (1 - 5*x - 2*x^2).

a(n) = sqrt(3/11)*(((5+sqrt(33))/2)^n - ((5-sqrt(33))/2)^n) = 3*A015535(n).

(End)