login
A259215
Number of (n+1) X (1+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0101.
2
7, 13, 24, 45, 85, 162, 311, 601, 1168, 2281, 4473, 8802, 17371, 34365, 68120, 135253, 268909, 535234, 1066287, 2125809, 4240672, 8463633, 16898609, 33750850, 67426675, 134731957, 269267496, 538217181, 1075920133, 2151008226, 4300670183
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = 3*a(n-1) - a(n-2) - 2*a(n-3).
Conjectures from Colin Barker, Dec 24 2018: (Start)
G.f.: x*(7 - 8*x - 8*x^2) / ((1 - 2*x)*(1 - x - x^2)).
a(n) = 2^(1+n) + (2^(-n)*((1-sqrt(5))^n*(-2+sqrt(5)) + (1+sqrt(5))^n*(2+sqrt(5)))) / sqrt(5).
(End)
EXAMPLE
Some solutions for n=4:
..1..0....0..1....1..1....0..1....1..0....0..1....0..0....1..0....1..0....0..0
..0..1....1..0....0..0....0..1....0..1....1..0....0..0....0..1....1..0....0..0
..0..1....0..1....1..1....1..0....0..1....0..1....1..1....0..1....0..1....0..0
..1..0....1..0....0..0....1..0....0..1....1..0....0..0....1..0....1..0....1..1
..0..1....0..1....1..1....0..1....1..0....1..0....1..1....1..0....1..0....0..0
CROSSREFS
Column 1 of A259222.
Sequence in context: A188557 A356966 A090992 * A215333 A034780 A137165
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jun 21 2015
STATUS
approved