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 A200833 #11 Oct 14 2017 10:45:48 %S A200833 56,194,676,2356,8210,28610,99700,347434,1210736,4219166,14702926, %T A200833 51236674,178549274,622207508,2168265232,7555958512,26330961818, %U A200833 91757987972,319757721532,1114289913490,3883071237050,13531704854780 %N A200833 Number of 0..3 arrays x(0..n+1) of n+2 elements without any two consecutive increases or two consecutive decreases. %C A200833 Column 3 of A200838. %H A200833 R. H. Hardin, <a href="/A200833/b200833.txt">Table of n, a(n) for n = 1..210</a> %F A200833 Empirical: a(n) = 4*a(n-1) -2*a(n-2) +a(n-3) -a(n-4). %F A200833 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 %e A200833 Some solutions for n=3 %e A200833 ..2....3....2....1....2....3....2....1....1....2....3....3....2....1....2....2 %e A200833 ..3....2....3....2....0....3....3....2....2....0....3....1....1....0....3....2 %e A200833 ..0....2....0....2....3....0....3....0....0....0....0....2....1....0....1....2 %e A200833 ..3....1....3....3....3....2....0....0....0....3....2....2....3....0....2....2 %e A200833 ..3....1....2....0....3....2....0....3....2....0....0....2....2....2....1....0 %K A200833 nonn %O A200833 1,1 %A A200833 _R. H. Hardin_ Nov 23 2011