login
A208309
Number of n X 3 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.
1
4, 18, 78, 336, 1446, 6222, 26772, 115194, 495654, 2132688, 9176478, 39484326, 169892196, 731008002, 3145363422, 13533793104, 58232875254, 250562996958, 1078116359028, 4638892804266, 19960114944246, 85883896308432
OFFSET
1,1
COMMENTS
Column 3 of A208314.
LINKS
FORMULA
Empirical: a(n) = 5*a(n-1) - 3*a(n-2).
Conjectures from Colin Barker, Jun 30 2018: (Start)
G.f.: 2*x*(2 - x) / (1 - 5*x + 3*x^2).
a(n) = (2^(-n)*((5-sqrt(13))^n*(-7+sqrt(13)) + (5+sqrt(13))^n*(7+sqrt(13)))) / (3*sqrt(13)).
(End)
EXAMPLE
Some solutions for n=4:
..0..1..0....0..0..0....0..1..1....0..1..1....0..1..1....0..1..0....0..0..0
..1..0..1....1..0..1....1..0..1....1..0..0....0..1..0....1..0..1....0..1..1
..0..1..0....0..1..0....1..1..0....1..1..1....0..1..1....1..0..1....1..0..1
..1..0..1....0..0..1....1..0..1....1..0..1....0..1..0....1..1..0....0..1..0
CROSSREFS
Cf. A208314.
Sequence in context: A219436 A219137 A240342 * A112619 A196810 A177755
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 25 2012
STATUS
approved