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

1,1

Comments

Column 2 of A208434.

Links

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

Index entries for linear recurrences with constant coefficients, signature (4).

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)

Example

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

Crossrefs

Cf. A208434.

Sequence in context: A363706 A259125 A067056 * A356373 A137482 A346033

Adjacent sequences: A208425 A208426 A208427 * A208429 A208430 A208431

Keyword

nonn

Author

R. H. Hardin, Feb 26 2012

Status

approved