A209530 Half the number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock having exactly two distinct clockwise edge differences.

9, 25, 65, 193, 513, 1537, 4097, 12289, 32769, 98305, 262145, 786433, 2097153, 6291457, 16777217, 50331649, 134217729, 402653185, 1073741825, 3221225473, 8589934593, 25769803777, 68719476737, 206158430209, 549755813889

Offset

1,1

Comments

Column 2 of A209534.

Links

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

Formula

Empirical: a(n) = a(n-1) + 8*a(n-2) - 8*a(n-3).

Conjectures from Colin Barker, Jul 10 2018: (Start)

G.f.: x*(9 + 16*x - 32*x^2) / ((1 - x)*(1 - 8*x^2)).

a(n) = 3*2^((3*(n - 1))/2 + 3/2) + 1 for n even.

a(n) = 2^((3*(n - 1))/2 + 3) + 1 for n odd.

(End)

Example

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

Crossrefs

Cf. A209534.

Sequence in context: A111440 A077118 A242116 * A147392 A147318 A146589

Adjacent sequences: A209527 A209528 A209529 * A209531 A209532 A209533

Keyword

nonn

Author

R. H. Hardin, Mar 10 2012

Status

approved