A200834 Number of 0..4 arrays x(0..n+1) of n+2 elements without any two consecutive increases or two consecutive decreases.

105, 435, 1817, 7587, 31677, 132263, 552247, 2305835, 9627715, 40199277, 167846875, 700822891, 2926195229, 12217949255, 51014464969, 213004292437, 889371840403, 3713456951747, 15505058633553, 64739364520389

Offset

1,1

Comments

Column 4 of A200838.

Links

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

Formula

Empirical: a(n) = 5*a(n-1) -4*a(n-2) +3*a(n-3) -3*a(n-4) +a(n-5) -a(n-6).

Empirical g.f.: x*(105 - 90*x + 62*x^2 - 73*x^3 + 20*x^4 - 25*x^5) / ((1 - x)*(1 - 4*x - 3*x^3 - x^5)). - Colin Barker, Oct 14 2017

Example

Some solutions for n=3
..2....4....1....2....3....1....1....1....0....2....4....2....0....1....1....3
..2....3....4....0....0....4....0....2....4....2....4....4....4....1....4....1
..2....3....4....0....2....3....1....2....3....2....1....4....3....3....3....1
..3....4....0....4....1....4....0....1....4....2....3....1....4....2....3....1
..3....3....1....0....2....2....0....2....3....0....1....2....2....4....4....0

Crossrefs

Sequence in context: A165056 A165060 A165069 * A143041 A078420 A152826

Adjacent sequences: A200831 A200832 A200833 * A200835 A200836 A200837

Keyword

nonn

Author

R. H. Hardin Nov 23 2011

Status

approved