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

1,1

Links

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

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

Adjacent sequences: A259212 A259213 A259214 * A259216 A259217 A259218

Keyword

nonn

Author

R. H. Hardin, Jun 21 2015

Status

approved