A206687 Number of n X 2 0..3 arrays with no element equal to another within two positions in the same row or column, and new values 0..3 introduced in row major order.

1, 4, 11, 36, 116, 376, 1216, 3936, 12736, 41216, 133376, 431616, 1396736, 4519936, 14626816, 47333376, 153174016, 495681536, 1604059136, 5190844416, 16797925376, 54359228416, 175910158336, 569257230336, 1842155094016, 5961339109376

Offset

1,2

Comments

Column 2 of A206692.

Links

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

Formula

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

Conjectures from Colin Barker, Feb 23 2018: (Start)

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

a(n) = ((1-sqrt(5))^n*(-5+3*sqrt(5)) + (1+sqrt(5))^n*(5+3*sqrt(5))) / (16*sqrt(5)) for n>2.

(End)

Example

All solutions for n=4:
..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1
..2..3....1..0....2..3....1..0....2..3....1..2....1..2....1..2....1..0
..1..2....2..3....1..0....2..3....3..2....2..0....3..0....2..3....2..3
..0..1....3..2....3..1....3..1....1..0....3..1....0..1....0..1....0..1

Crossrefs

Cf. A206692.

Sequence in context: A114248 A149237 A054577 * A106640 A109268 A256960

Adjacent sequences: A206684 A206685 A206686 * A206688 A206689 A206690

Keyword

nonn

Author

R. H. Hardin, Feb 11 2012

Status

approved