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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A008524 A302885

Adjacent sequences:  A205217 A205218 A205219 * A205221 A205222 A205223

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 23 2012

STATUS

approved

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Last modified September 18 05:32 EDT 2019. Contains 327165 sequences. (Running on oeis4.)