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
Keywords
Examples
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
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
Comments