|
|
A234789
|
|
Number of (n+1) X (1+1) 0..3 arrays with each 2 X 2 subblock having the number of clockwise edge increases less than or equal to the number of counterclockwise edge increases.
|
|
1
|
|
|
204, 2504, 30536, 371976, 4530424, 55175944, 671983416, 8184025736, 99672501944, 1213902270984, 14784004509496, 180053035925896, 2192849421966264, 26706512126351624, 325256163423006776, 3961265003235768456
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = 15*a(n-1) - 36*a(n-2) + 20*a(n-3).
G.f.: 4*x*(51 - 139*x + 80*x^2) / ((1 - 2*x)*(1 - 13*x + 10*x^2)).
a(n) = (1/129)*2^(-1-n)*(-129*2^(1+2*n) + (2193-191*sqrt(129))*(13-sqrt(129))^n + (13+sqrt(129))^n*(2193+191*sqrt(129))).
(End)
|
|
EXAMPLE
|
Some solutions for n=3:
..2..3....1..2....2..0....2..3....1..0....1..0....2..1....0..1....3..2....1..0
..2..3....0..1....2..0....3..1....3..2....3..2....0..2....0..1....2..0....2..0
..2..2....2..0....3..2....3..1....0..0....2..0....2..1....0..1....2..3....3..0
..0..0....1..3....2..0....0..0....1..1....2..3....2..0....2..3....3..3....1..3
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|