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 A200840 #9 Oct 15 2017 01:11:41 %S A200840 32,191,676,1817,4108,8239,15128,25953,42184,65615,98396,143065, %T A200840 202580,280351,380272,506753,664752,859807,1098068,1386329,1732060, %U A200840 2143439,2629384,3199585,3864536,4635567,5524876,6545561,7711652,9038143 %N A200840 Number of 0..n arrays x(0..4) of 5 elements without any two consecutive increases or two consecutive decreases. %C A200840 Row 3 of A200838. %H A200840 R. H. Hardin, <a href="/A200840/b200840.txt">Table of n, a(n) for n = 1..210</a> %F A200840 Empirical: a(n) = (4/15)*n^5 + (17/6)*n^4 + (28/3)*n^3 + (73/6)*n^2 + (32/5)*n + 1. %F A200840 Conjectures from _Colin Barker_, Oct 14 2017: (Start) %F A200840 G.f.: x*(32 - x + 10*x^2 - 14*x^3 + 6*x^4 - x^5) / (1 - x)^6. %F A200840 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6. %F A200840 (End) %e A200840 Some solutions for n=3 %e A200840 ..2....1....1....1....2....3....1....0....0....0....2....2....1....1....2....3 %e A200840 ..3....3....3....3....0....0....0....2....0....0....0....2....3....1....0....3 %e A200840 ..0....3....0....0....0....1....3....2....2....3....0....0....1....2....3....2 %e A200840 ..3....1....2....3....3....1....3....0....0....0....0....2....2....1....3....3 %e A200840 ..0....2....0....2....0....0....1....0....2....0....0....0....2....3....0....2 %K A200840 nonn %O A200840 1,1 %A A200840 _R. H. Hardin_ Nov 23 2011