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

Author

R. H. Hardin Nov 23 2011

Keywords

• nonn

Comments

Column 3 of A200838.

Examples

			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
		

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