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 A200844 #11 Oct 15 2017 01:12:00 %S A200844 512,11235,99700,552247,2276028,7642875,22063924,56687801,132734964, %T A200844 288116455,587136848,1134248583,2093008152,3711583751,6356379032, %U A200844 10555568481,17054586712,26885876603,41455479708,62649346759,92962556324 %N A200844 Number of 0..n arrays x(0..8) of 9 elements without any two consecutive increases or two consecutive decreases. %C A200844 Row 7 of A200838. %H A200844 R. H. Hardin, <a href="/A200844/b200844.txt">Table of n, a(n) for n = 1..210</a> %F A200844 Empirical: a(n) = (124/2835)*n^9 + (1123/1120)*n^8 + (244/27)*n^7 + (1991/48)*n^6 + (57133/540)*n^5 + (74183/480)*n^4 + (291427/2268)*n^3 + (9739/168)*n^2 + (568/45)*n + 1. %F A200844 Conjectures from _Colin Barker_, Oct 14 2017: (Start) %F A200844 G.f.: x*(512 + 6115*x + 10390*x^2 - 618*x^3 - 622*x^4 + 36*x^5 + 94*x^6 - 44*x^7 + 10*x^8 - x^9) / (1 - x)^10. %F A200844 a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n > 10. %F A200844 (End) %e A200844 Some solutions for n=3: %e A200844 1 2 1 1 3 2 3 1 1 2 2 1 3 0 3 0 %e A200844 1 3 1 0 2 2 3 1 0 3 1 3 3 2 2 1 %e A200844 0 0 3 3 3 3 2 0 2 1 3 3 1 1 3 1 %e A200844 0 1 2 1 2 1 3 3 0 1 0 0 3 2 3 2 %e A200844 3 1 2 2 2 3 3 1 1 3 3 0 3 2 0 2 %e A200844 1 3 2 2 0 1 3 1 0 1 1 2 2 0 0 1 %e A200844 2 0 3 0 1 3 0 3 2 3 3 0 3 1 0 2 %e A200844 1 1 0 3 1 1 2 2 0 0 3 3 3 1 2 1 %e A200844 3 0 2 2 2 3 0 2 1 1 2 3 0 1 1 1 %K A200844 nonn %O A200844 1,1 %A A200844 _R. H. Hardin_, Nov 23 2011