A243722 Number of length n+2 0..3 arrays with no three unequal elements in a row and no three equal elements in a row and new values 0..3 introduced in 0..3 order.

3, 6, 12, 25, 53, 115, 253, 564, 1268, 2871, 6531, 14911, 34127, 78250, 179644, 412797, 949145, 2183355, 5024025, 11563144, 26617508, 61278283, 141084439, 324844263, 747976187, 1722312558, 3965923308, 9132346753, 21029284637, 48424978627

Offset

1,1

Links

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

Formula

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

Empirical g.f.: x*(3 - 9*x^2 - 5*x^3) / ((1 - x - x^2)*(1 - x - 3*x^2)). - Colin Barker, Nov 03 2018

Example

Some solutions for n=6:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....0....1....1....1....1....0....1....1....1....1....1....1....1....1....0
..0....1....0....0....0....1....1....1....0....1....0....1....1....0....1....1
..1....0....1....0....0....0....1....0....0....2....1....2....2....1....2....0
..1....1....0....1....1....1....2....0....2....2....1....2....2....1....1....0
..0....0....0....1....1....1....2....2....0....0....0....1....3....2....1....1
..0....0....2....2....0....0....0....0....0....2....0....1....2....1....2....1
..1....2....2....2....0....1....0....2....3....0....2....2....2....2....1....0

Crossrefs

Column 3 of A243729.

Sequence in context: A265700 A293313 A267539 * A187260 A243723 A243724

Adjacent sequences: A243719 A243720 A243721 * A243723 A243724 A243725

Keyword

nonn

Author

R. H. Hardin, Jun 09 2014

Status

approved