A185762 Number of (n+1) X 3 binary arrays with no 2 X 2 subblock trace equal to any horizontal or vertical neighbor 2 X 2 subblock trace.

40, 120, 368, 1128, 3456, 10592, 32456, 99464, 304792, 934032, 2862248, 8771232, 26878752, 82368392, 252412136, 773501240, 2370342448, 7263762024, 22259317952, 68212232544, 209031902280, 640564615496, 1962968261720, 6015387856976

Offset

1,1

Comments

Column 2 of A185769.

Links

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

Formula

Empirical: a(n) = a(n-1) + 6*a(n-2) + a(n-3).

Empirical g.f.: 8*x*(5 + 10*x + x^2) / (1 - x - 6*x^2 - x^3). - Colin Barker, Apr 16 2018

Example

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

Crossrefs

Cf. A185769.

Sequence in context: A234921 A199807 A199810 * A234914 A043470 A044291

Adjacent sequences: A185759 A185760 A185761 * A185763 A185764 A185765

Keyword

nonn

Author

R. H. Hardin, Feb 03 2011

Status

approved