|
|
A234779
|
|
Number of (n+1) X (1+1) 0..3 arrays with no adjacent elements equal and with each 2 X 2 subblock having the number of clockwise edge increases equal to the number of counterclockwise edge increases.
|
|
1
|
|
|
76, 484, 3084, 19652, 125228, 797988, 5085004, 32403076, 206481516, 1315758308, 8384382092, 53427641412, 340455961516, 2169481164964, 13824544308684, 88093885500932, 561359021271788, 3577137606898788, 22794527163204364
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = 7*a(n-1) - 4*a(n-2).
G.f.: 4*x*(19 - 12*x) / (1 - 7*x + 4*x^2).
a(n) = (2^(1-n)*((7-sqrt(33))^n*(-17+3*sqrt(33)) + (7+sqrt(33))^n*(17+3*sqrt(33)))) / sqrt(33).
(End)
|
|
EXAMPLE
|
Some solutions for n=5:
..3..2....2..0....1..0....2..3....3..2....3..2....1..0....1..2....2..0....2..1
..2..1....0..3....0..1....1..2....2..1....2..1....2..1....2..0....1..3....0..2
..0..2....2..1....2..3....3..0....1..3....0..3....0..3....1..3....3..1....1..3
..2..0....1..3....0..1....2..3....2..0....3..0....3..2....2..0....1..3....0..1
..0..3....0..1....2..3....0..1....0..1....0..2....0..3....3..2....0..1....1..3
..3..0....3..0....3..2....1..0....3..0....1..3....3..0....2..1....1..3....2..1
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|