A183682 Number of (n+1) X 3 binary arrays with every 2 X 2 subblock nonsingular.

12, 32, 80, 208, 528, 1360, 3472, 8912, 22800, 58448, 149648, 383440, 982032, 2515792, 6443920, 16507088, 42282768, 108311120, 277442192, 710686672, 1820455440, 4663202128, 11945023888, 30597832400, 78377927952, 200769257552

Offset

1,1

Comments

Column 2 of A183688.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = a(n-1) + 4*a(n-2).

Conjectures from Colin Barker, Feb 27 2018: (Start)

G.f.: 4*x*(3 + 5*x) / (1 - x - 4*x^2).

a(n) = (2^(-1-n)*((1-sqrt(17))^n*(-19+5*sqrt(17)) + (1+sqrt(17))^n*(19+5*sqrt(17)))) / sqrt(17).

(End)

Example

Some solutions for 5 X 3:
..0..1..1....0..1..1....0..1..0....1..1..1....1..1..0....1..1..0....1..0..1
..1..0..1....1..0..1....1..0..1....1..0..1....1..0..1....1..0..1....1..1..0
..1..1..0....0..1..0....0..1..0....1..1..0....1..1..1....0..1..1....0..1..1
..0..1..1....1..0..1....1..0..1....1..0..1....0..1..0....1..0..1....1..1..0
..1..1..0....0..1..0....0..1..0....0..1..0....1..1..1....1..1..0....1..0..1

Crossrefs

Cf. A183688.

Sequence in context: A081268 A332595 A188183 * A243027 A242543 A194644

Adjacent sequences: A183679 A183680 A183681 * A183683 A183684 A183685

Keyword

nonn

Author

R. H. Hardin, Jan 06 2011

Status

approved