A209841 Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock having one or two distinct values, and new values 0..3 introduced in row major order.

8, 41, 227, 1331, 8123, 50987, 326123, 2111531, 13777067, 90322091, 593895083, 3912075947, 25797704363, 170233203371, 1123784731307, 7420419975851, 49004773878443, 323658783566507, 2137765638482603, 14120404331440811

Offset

1,1

Comments

Column 1 of A209848.

Links

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

Formula

Empirical: a(n) = 11*a(n-1) - 30*a(n-2) + 4*a(n-3) + 16*a(n-4).

Empirical g.f.: x*(8 - 47*x + 16*x^2 + 32*x^3) / ((1 - x)*(1 - 4*x)*(1 - 6*x - 4*x^2)). - Colin Barker, Jul 13 2018

Example

Some solutions for n=4:
..0..0....0..1....0..1....0..0....0..0....0..0....0..0....0..1....0..1....0..1
..0..0....0..0....0..1....1..0....0..0....0..0....1..0....0..0....0..0....0..0
..1..0....0..1....0..0....0..1....0..0....0..0....0..1....0..0....0..1....2..2
..0..0....0..1....0..0....1..0....1..0....0..0....1..0....1..0....0..0....0..0
..2..0....0..0....0..0....0..1....1..0....0..0....0..0....0..0....2..2....2..2

Crossrefs

Cf. A209848.

Sequence in context: A265149 A209822 A051737 * A196927 A188209 A026953

Adjacent sequences: A209838 A209839 A209840 * A209842 A209843 A209844

Keyword

nonn

Author

R. H. Hardin, Mar 14 2012

Status

approved