A183682 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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