|
|
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.
|
|
1
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = a(n-1) + 8*a(n-2) - 8*a(n-3).
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|