A243038 Number of length n+3 0..2 arrays with no four elements in a row with pattern abab (with a!=b) and new values 0..2 introduced in 0..2 order.

13, 36, 101, 285, 806, 2281, 6457, 18280, 51753, 146521, 414826, 1174445, 3325061, 9413836, 26652237, 75457205, 213632718, 604832081, 1712386801, 4848070480, 13725746641, 38860021041, 110019605842, 311485000405, 881869233533

Offset

1,1

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - a(n-3) - a(n-4).

Empirical g.f.: x*(13 - 3*x - 7*x^2 - 5*x^3) / ((1 - x)*(1 - 2*x - 2*x^2 - x^3)). - Colin Barker, Nov 01 2018

Example

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

Crossrefs

Column 2 of A243044.

Sequence in context: A051865 A081928 A034129 * A297303 A225131 A357444

Adjacent sequences: A243035 A243036 A243037 * A243039 A243040 A243041

Keyword

nonn

Author

R. H. Hardin, May 29 2014

Status

approved