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 A267233 #7 Feb 05 2018 17:10:08 %S A267233 6,47,176,470,1030,1981,3472,5676,8790,13035,18656,25922,35126,46585, %T A267233 60640,77656,98022,122151,150480,183470,221606,265397,315376,372100, %U A267233 436150,508131,588672,678426,778070,888305,1009856,1143472,1289926 %N A267233 Number of length-4 0..n arrays with no following elements greater than or equal to the first repeated value. %C A267233 Row 4 of A267232. %H A267233 R. H. Hardin, <a href="/A267233/b267233.txt">Table of n, a(n) for n = 1..210</a> %F A267233 Empirical: a(n) = n^4 + (17/6)*n^3 + 2*n^2 + (1/6)*n. %F A267233 Conjectures from _Colin Barker_, Feb 05 2018: (Start) %F A267233 G.f.: x*(6 + 17*x + x^2) / (1 - x)^5. %F A267233 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 A267233 (End) %e A267233 Some solutions for n=6: %e A267233 ..4....5....2....2....0....4....4....5....0....4....3....2....0....4....0....3 %e A267233 ..3....3....4....0....5....2....0....6....3....5....4....4....3....3....2....6 %e A267233 ..1....3....2....5....5....3....1....2....5....5....2....1....0....2....4....4 %e A267233 ..4....0....6....4....4....1....4....1....4....3....3....3....6....4....2....6 %Y A267233 Cf. A267232. %K A267233 nonn %O A267233 1,1 %A A267233 _R. H. Hardin_, Jan 12 2016