A200833 Number of 0..3 arrays x(0..n+1) of n+2 elements without any two consecutive increases or two consecutive decreases.

56, 194, 676, 2356, 8210, 28610, 99700, 347434, 1210736, 4219166, 14702926, 51236674, 178549274, 622207508, 2168265232, 7555958512, 26330961818, 91757987972, 319757721532, 1114289913490, 3883071237050, 13531704854780

Offset

1,1

Comments

Column 3 of A200838.

Links

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

Formula

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

Empirical g.f.: 2*x*(28 - 15*x + 6*x^2 - 8*x^3) / (1 - 4*x + 2*x^2 - x^3 + x^4). - Colin Barker, Oct 14 2017

Example

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

Crossrefs

Sequence in context: A234107 A136547 A264303 * A241611 A179403 A158481

Adjacent sequences: A200830 A200831 A200832 * A200834 A200835 A200836

Keyword

nonn

Author

R. H. Hardin Nov 23 2011

Status

approved