A185858 1/128 the number of (n+2) X 3 binary arrays with no 3 X 3 subblock trace equal to any horizontal or vertical neighbor 3 X 3 subblock trace.

4, 22, 124, 694, 3892, 21814, 122284, 685462, 3842404, 21538774, 120736732, 676795894, 3793814164, 21266419702, 119210006284, 668237802454, 3745841266372, 20997505287574, 117702592547644, 659787917778742

Offset

1,1

Comments

Column 1 of A185866.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) + 9*a(n-2).

Conjectures from Colin Barker, Apr 17 2018: (Start)

G.f.: 2*x*(2 + 3*x) / (1 - 4*x - 9*x^2).

a(n) = ((2 - sqrt(13))^n*(-4+sqrt(13)) + (2+sqrt(13))^n*(4+sqrt(13))) / (3*sqrt(13)).

(End)

Example

Some solutions for 4 X 3:
..0..0..0....1..0..0....0..1..1....0..0..0....0..0..1....0..1..0....1..0..0
..0..1..1....0..1..0....0..1..1....1..0..1....1..0..1....1..1..0....1..1..0
..0..0..1....0..0..1....0..1..0....0..0..0....0..1..1....0..1..0....0..0..1
..0..1..0....0..1..0....0..1..1....1..0..0....1..1..0....1..0..0....1..0..1

Crossrefs

Cf. A185866.

Sequence in context: A098834 A065983 A236576 * A180034 A260346 A136777

Adjacent sequences: A185855 A185856 A185857 * A185859 A185860 A185861

Keyword

nonn

Author

R. H. Hardin, Feb 05 2011

Status

approved