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 A224185 #8 Aug 29 2018 05:57:48 %S A224185 22,158,684,2205,5852,13524,28176,54153,97570,166738,272636,429429, %T A224185 655032,971720,1406784,1993233,2770542,3785446,5092780,6756365, %U A224185 8849940,11458140,14677520,18617625,23402106,29169882,36076348,44294629,54016880 %N A224185 Number of n X 3 0..2 arrays with rows unimodal and columns nondecreasing. %C A224185 Column 3 of A224190. %H A224185 R. H. Hardin, <a href="/A224185/b224185.txt">Table of n, a(n) for n = 1..210</a> %F A224185 Empirical: a(n) = (23/360)*n^6 + (27/40)*n^5 + (205/72)*n^4 + (49/8)*n^3 + (319/45)*n^2 + (21/5)*n + 1. %F A224185 Conjectures from _Colin Barker_, Aug 29 2018: (Start) %F A224185 G.f.: x*(22 + 4*x + 40*x^2 - 35*x^3 + 21*x^4 - 7*x^5 + x^6) / (1 - x)^7. %F A224185 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7. %F A224185 (End) %e A224185 Some solutions for n=3. %e A224185 ..1..0..0....0..1..0....2..1..0....0..2..1....0..0..0....0..0..1....0..0..0 %e A224185 ..2..0..0....1..2..0....2..2..0....0..2..1....1..0..0....0..0..2....1..1..0 %e A224185 ..2..0..0....1..2..2....2..2..1....1..2..1....2..2..0....0..0..2....2..2..0 %Y A224185 Cf. A224190. %K A224185 nonn %O A224185 1,1 %A A224185 _R. H. Hardin_, Apr 01 2013