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 A200865 #15 Oct 15 2017 20:28:44
%S A200865 17,37,77,163,343,723,1523,3209,6761,14245,30013,63235,133231,280707,
%T A200865 591427,1246089,2625409,5531525,11654477,24555043,51735495,109002515,
%U A200865 229659507,483874057,1019483609,2147969733,4525598973,9535072003
%N A200865 Number of 0..2 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors or less than both neighbors.
%C A200865 Column 2 of A200871.
%H A200865 R. H. Hardin, <a href="/A200865/b200865.txt">Table of n, a(n) for n = 1..210</a>
%F A200865 Empirical: a(n) = 2*a(n-1) +a(n-4).
%F A200865 Empirical g.f.: x*(17 + 3*x + 3*x^2 + 9*x^3) / (1 - 2*x - x^4). - _Colin Barker_, Oct 15 2017
%e A200865 Some solutions for n=3
%e A200865 ..0....2....0....2....2....0....0....0....0....1....2....2....0....0....0....2
%e A200865 ..0....2....0....2....1....1....0....1....1....0....2....0....2....0....2....1
%e A200865 ..1....2....2....1....0....2....0....1....1....0....1....0....2....0....2....1
%e A200865 ..2....2....2....1....0....2....0....2....0....1....1....1....2....1....2....1
%e A200865 ..2....2....0....2....0....2....2....2....0....1....1....2....2....2....0....1
%t A200865 a[0,x_,y_] := 1; a[n_,x_,y_] := a[n,x,y] = Sum[If[z <=x<= y || y <=x<= z, a[n-1, z, x], 0], {z, 3}]; a[n_] := Sum[a[n, x, y], {x, 3}, {y, 3}]; Array[a, 25] (* _Giovanni Resta_, Mar 05 2014 *)
%K A200865 nonn
%O A200865 1,1
%A A200865 _R. H. Hardin_, Nov 23 2011