A210079 Number of (n+1) X 2 0..3 arrays containing all values 0..3 with every 2 X 2 subblock having one, three or four distinct values, and new values 0..3 introduced in row major order.

1, 51, 762, 9405, 109194, 1239185, 13937206, 156188077, 1747769906, 19546177481, 218541500622, 2443222239685, 27313318510154, 305336555697185, 3413345205975206, 38157545443338717, 426560032707189986

Offset

1,2

Comments

Column 1 of A210086.

Links

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

Formula

Empirical: a(n) = 17*a(n-1) - 71*a(n-2) + 67*a(n-3) - 8*a(n-4) - 4*a(n-5).

Empirical g.f.: x*(1 + 34*x - 34*x^2 + 5*x^3 + 2*x^4) / ((1 - x)*(1 - 5*x + 2*x^2)*(1 - 11*x - 2*x^2)). - Colin Barker, Jul 14 2018

Example

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

Crossrefs

Cf. A210086.

Sequence in context: A210176 A224474 A201140 * A201832 A317651 A201212

Adjacent sequences: A210076 A210077 A210078 * A210080 A210081 A210082

Keyword

nonn

Author

R. H. Hardin, Mar 17 2012

Status

approved