A243723 Number of length n+2 0..4 arrays with no three unequal elements in a row and no three equal elements in a row and new values 0..4 introduced in 0..4 order.

3, 6, 12, 25, 53, 116, 259, 593, 1382, 3281, 7897, 19252, 47391, 117645, 293934, 738341, 1862341, 4713220, 11959211, 30407929, 77440630, 197470825, 504041249, 1287558068, 3291018759, 8415888789, 21529314366, 55091691997, 141006790829

Offset

1,1

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 13*a(n-3) + 6*a(n-4) + 8*a(n-5).

Empirical g.f.: x*(3 - 6*x - 12*x^2 + 16*x^3 + 13*x^4) / ((1 - 2*x)*(1 - x - x^2)*(1 - x - 4*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....1....1....0....0....1....1....1....0....1....1....1....0....1....1....1
..1....1....0....1....1....0....0....1....1....1....1....0....1....0....0....1
..2....2....1....0....1....0....0....0....1....0....2....0....0....1....1....0
..1....1....1....1....0....1....2....0....0....1....2....2....1....0....0....0
..2....2....2....0....1....1....2....1....0....1....3....2....0....1....1....2
..2....2....2....1....1....2....0....1....2....0....2....1....1....0....1....2
..0....1....0....1....0....2....0....2....0....1....3....2....0....1....2....1

Crossrefs

Column 4 of A243729.

Sequence in context: A267539 A243722 A187260 * A243724 A243725 A243726

Adjacent sequences: A243720 A243721 A243722 * A243724 A243725 A243726

Keyword

nonn

Author

R. H. Hardin, Jun 09 2014

Status

approved