A259215 Number of (n+1) X (1+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0101.

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

Author

R. H. Hardin, Jun 21 2015

Keywords

• nonn

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Crossrefs

Column 1 of A259222.

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)