This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A200834 #8 Oct 14 2017 10:45:55 %S A200834 105,435,1817,7587,31677,132263,552247,2305835,9627715,40199277, %T A200834 167846875,700822891,2926195229,12217949255,51014464969,213004292437, %U A200834 889371840403,3713456951747,15505058633553,64739364520389 %N A200834 Number of 0..4 arrays x(0..n+1) of n+2 elements without any two consecutive increases or two consecutive decreases. %C A200834 Column 4 of A200838. %H A200834 R. H. Hardin, <a href="/A200834/b200834.txt">Table of n, a(n) for n = 1..210</a> %F A200834 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). %F A200834 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 %e A200834 Some solutions for n=3 %e A200834 ..2....4....1....2....3....1....1....1....0....2....4....2....0....1....1....3 %e A200834 ..2....3....4....0....0....4....0....2....4....2....4....4....4....1....4....1 %e A200834 ..2....3....4....0....2....3....1....2....3....2....1....4....3....3....3....1 %e A200834 ..3....4....0....4....1....4....0....1....4....2....3....1....4....2....3....1 %e A200834 ..3....3....1....0....2....2....0....2....3....0....1....2....2....4....4....0 %K A200834 nonn %O A200834 1,1 %A A200834 _R. H. Hardin_ Nov 23 2011