A208428 Number of n X 2 0..2 arrays with new values 0..2 introduced in row major order and no element equal to any knight-move neighbor (colorings ignoring permutations of colors).

2, 14, 54, 216, 864, 3456, 13824, 55296, 221184, 884736, 3538944, 14155776, 56623104, 226492416, 905969664, 3623878656, 14495514624, 57982058496, 231928233984, 927712935936, 3710851743744, 14843406974976, 59373627899904

Offset: 1

Author

R. H. Hardin, Feb 26 2012

Keywords

• nonn

Comments

Column 2 of A208434.

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210
• Index entries for linear recurrences with constant coefficients, signature (4).

Crossrefs

Cf. A208434.

Formula

Empirical: a(n) = 4*a(n-1) for n>3.

Conjectures from Colin Barker, Feb 23 2018: (Start)

G.f.: 2*x*(1 + 3*x - x^2) / (1 - 4*x).

a(n) = 27*2^(2*n - 5) for n>2.

(End)