A205220 Number of (n+1) X 3 0..1 arrays with the number of equal 2 X 2 subblock diagonal pairs and equal antidiagonal pairs differing from each horizontal or vertical neighbor, and new values 0..1 introduced in row major order.

20, 52, 132, 340, 868, 2228, 5700, 14612, 37412, 95860, 245508, 628948, 1610980, 4126772, 10570692, 27077780, 69360548, 177671668, 455113860, 1165800532, 2986255972, 7649458100, 19594481988, 50192314388, 128570242340, 329339499892

Offset

1,1

Comments

Column 2 of A205226.

References

Equals A205219(n+1).

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

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

Conjectures from Colin Barker, Jun 11 2018: (Start)

G.f.: 4*x*(5 + 8*x) / (1 - x - 4*x^2).

a(n) = (2^(2-n)*((1-sqrt(17))^n*(-4+sqrt(17)) + (1+sqrt(17))^n*(4+sqrt(17)))) / sqrt(17).

(End)

Example

Some solutions for n=4:
..0..0..0....0..1..0....0..1..1....0..0..1....0..1..1....0..0..1....0..1..0
..0..0..1....1..1..0....0..0..0....1..0..1....0..1..0....0..0..1....1..1..0
..1..0..1....0..0..0....0..0..1....0..1..1....1..1..0....1..1..1....0..0..1
..0..1..1....1..0..0....1..0..1....0..0..0....1..1..1....1..0..0....1..0..1
..1..1..1....0..1..0....1..0..0....1..1..0....1..0..0....0..1..0....0..1..1

Crossrefs

Cf. A205226.

Sequence in context: A211143 A183047 A209982 * A188250 A329627 A329628

Adjacent sequences: A205217 A205218 A205219 * A205221 A205222 A205223

Keyword

nonn

Author

R. H. Hardin, Jan 23 2012

Status

approved