A209789 Half the number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock having exactly one duplicate clockwise edge difference.

30, 204, 1380, 9348, 63300, 428676, 2902980, 19659012, 133130820, 901562244, 6105381060, 41345652228, 279992833860, 1896111996036, 12840473986500, 86955713884932, 588864257262660, 3987789852932484, 27005320351814340

Offset

1,1

Comments

Column 1 of A209796.

Links

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

Formula

Empirical: a(n) = 5*a(n-1) + 12*a(n-2).

Conjectures from Colin Barker, Jul 13 2018: (Start)

G.f.: 6*x*(5 + 9*x) / (1 - 5*x - 12*x^2).

a(n) = (2^(-2-n)*(3*(5+sqrt(73))^n*(25+3*sqrt(73)) + (5-sqrt(73))^n*(-75+9*sqrt(73)))) / sqrt(73).

(End)

Example

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

Crossrefs

Cf. A209796.

Sequence in context: A165030 A165016 A209796 * A280482 A371721 A203617

Adjacent sequences: A209786 A209787 A209788 * A209790 A209791 A209792

Keyword

nonn

Author

R. H. Hardin, Mar 13 2012

Status

approved