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 A200872 #10 Oct 16 2017 12:22:22 %S A200872 10,37,94,195,356,595,932,1389,1990,2761,3730,4927,6384,8135,10216, %T A200872 12665,15522,18829,22630,26971,31900,37467,43724,50725,58526,67185, %U A200872 76762,87319,98920,111631,125520,140657,157114,174965,194286,215155,237652,261859 %N A200872 Number of 0..n arrays x(0..3) of 4 elements without any interior element greater than both neighbors or less than both neighbors. %C A200872 Row 2 of A200871. %H A200872 R. H. Hardin, <a href="/A200872/b200872.txt">Table of n, a(n) for n = 1..210</a> %F A200872 Empirical: a(n) = (1/12)*n^4 + (3/2)*n^3 + (47/12)*n^2 + (7/2)*n + 1. %F A200872 Conjectures from _Colin Barker_, Oct 16 2017: (Start) %F A200872 G.f.: x*(10 - 13*x + 9*x^2 - 5*x^3 + x^4) / (1 - x)^5. %F A200872 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5. %F A200872 (End) %e A200872 Some solutions for n=3 %e A200872 ..1....0....2....0....3....0....2....2....1....0....0....0....3....0....3....0 %e A200872 ..2....2....3....1....3....0....2....2....3....2....0....0....2....2....1....1 %e A200872 ..2....3....3....1....2....1....1....2....3....2....0....1....2....2....1....3 %e A200872 ..1....3....0....0....1....1....0....2....1....1....0....2....2....0....1....3 %K A200872 nonn %O A200872 1,1 %A A200872 _R. H. Hardin_, Nov 23 2011