A185761 Number of (n+1) X 2 binary arrays with no 2 X 2 subblock trace equal to any horizontal or vertical neighbor 2 X 2 subblock trace.

16, 40, 104, 264, 680, 1736, 4456, 11400, 29224, 74824, 191720, 491016, 1257896, 3221960, 8253544, 21141384, 54155560, 138721096, 355343336, 910227720, 2331601064, 5972511944, 15298916200, 39188963976, 100384628776, 257140484680

Offset

1,1

Comments

Column 1 of A185769.

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 22 2018: (Start)

G.f.: 8*x*(2 + 3*x) / (1 - x - 4*x^2).

a(n) = (2^(-n)*((1-sqrt(17))^n*(-13+3*sqrt(17)) + (1+sqrt(17))^n*(13+3*sqrt(17)))) / sqrt(17).

(End)

Example

Some solutions for 3 X 2:
..0..1....0..0....1..1....0..0....1..1....1..1....1..0....0..0....0..1....1..1
..1..0....0..1....0..0....0..0....0..1....0..1....0..1....0..0....1..1....1..1
..1..1....1..0....1..0....1..1....0..1....1..1....0..0....0..1....1..1....0..0

Crossrefs

Cf. A185769.

Sequence in context: A205065 A368078 A185790 * A205248 A205186 A197903

Adjacent sequences: A185758 A185759 A185760 * A185762 A185763 A185764

Keyword

nonn

Author

R. H. Hardin, Feb 03 2011

Status

approved