A209944 Half the number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock having at most one duplicate clockwise edge difference.

34, 258, 1956, 14832, 112464, 852768, 6466176, 49030272, 371775744, 2819017728, 21375415296, 162080704512, 1228989210624, 9318903717888, 70661292834816, 535794601623552, 4062703123759104, 30805753962037248, 233586961257332736

Offset

1,1

Comments

Column 1 of A209951.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) + 12*a(n-2).

Conjectures from Colin Barker, Jul 14 2018: (Start)

G.f.: 2*x*(17 + 27*x) / (1 - 6*x - 12*x^2).

a(n) = ((3-sqrt(21))^n*(-41+9*sqrt(21)) + (3+ sqrt(21))^n*(41+9*sqrt(21))) / (4*sqrt(21)).

(End)

Example

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

Crossrefs

Cf. A209951.

Sequence in context: A183319 A190422 A209951 * A371403 A081219 A254700

Adjacent sequences: A209941 A209942 A209943 * A209945 A209946 A209947

Keyword

nonn

Author

R. H. Hardin, Mar 16 2012

Status

approved