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 A200887 #10 Oct 16 2017 09:57:36 %S A200887 12,51,144,325,636,1127,1856,2889,4300,6171,8592,11661,15484,20175, %T A200887 25856,32657,40716,50179,61200,73941,88572,105271,124224,145625, %U A200887 169676,196587,226576,259869,296700,337311,381952,430881,484364,542675,606096,674917 %N A200887 Number of 0..n arrays x(0..3) of 4 elements without any interior element greater than both neighbors. %C A200887 Row 2 of A200886. %H A200887 R. H. Hardin, <a href="/A200887/b200887.txt">Table of n, a(n) for n = 1..210</a> %F A200887 Empirical: a(n) = (1/3)*n^4 + (7/3)*n^3 + (14/3)*n^2 + (11/3)*n + 1. %F A200887 Conjectures from _Colin Barker_, Oct 16 2017: (Start) %F A200887 G.f.: x*(12 - 9*x + 9*x^2 - 5*x^3 + x^4) / (1 - x)^5. %F A200887 a(n) = (1+n)^2 * (3+5*n+n^2) / 3. %F A200887 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 A200887 (End) %e A200887 Some solutions for n=3 %e A200887 ..3....1....0....0....3....1....3....1....2....2....0....1....3....1....3....2 %e A200887 ..2....1....1....0....1....1....1....0....2....3....3....0....3....3....3....0 %e A200887 ..1....3....1....2....2....0....3....1....2....3....3....0....2....3....1....2 %e A200887 ..1....3....0....3....3....1....3....2....2....3....2....2....2....0....2....2 %K A200887 nonn %O A200887 1,1 %A A200887 _R. H. Hardin_, Nov 23 2011