|
|
A259243
|
|
Number of (n+1) X (1+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0111.
|
|
1
|
|
|
9, 21, 48, 111, 255, 588, 1353, 3117, 7176, 16527, 38055, 87636, 201801, 464709, 1070112, 2464239, 5674575, 13067292, 30091017, 69292893, 159565944, 367444623, 846142455, 1948476324, 4486903689, 10332332661, 23793043728, 54790041711
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = a(n-1) + 3*a(n-2).
G.f.: 3*x*(3 + 4*x) / (1 - x - 3*x^2).
a(n) = (2^(-n)*((1-sqrt(13))^n*(-7+2*sqrt(13)) + (1+sqrt(13))^n*(7+2*sqrt(13)))) / sqrt(13).
(End)
|
|
EXAMPLE
|
Some solutions for n=4:
..1..0....1..1....1..0....0..1....1..0....1..1....1..1....1..0....0..1....0..1
..1..0....1..0....1..1....1..1....1..1....0..1....0..1....1..1....1..1....1..1
..1..1....1..0....0..1....0..1....0..0....1..1....0..1....0..1....1..0....0..0
..0..0....1..1....1..1....1..1....1..1....0..1....1..1....1..1....1..1....1..1
..1..1....0..1....0..0....0..1....0..0....0..1....0..0....1..0....1..0....0..0
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|