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 A189807 #10 May 03 2018 07:02:28 %S A189807 14,44,94,158,238,330,434,550,678,818,970,1134,1310,1498,1698,1910, %T A189807 2134,2370,2618,2878,3150,3434,3730,4038,4358,4690,5034,5390,5758, %U A189807 6138,6530,6934,7350,7778,8218,8670,9134,9610,10098,10598,11110,11634,12170,12718 %N A189807 Number of right triangles on an (n+1) X 3 grid. %C A189807 Column 2 of A189814. %H A189807 R. H. Hardin, <a href="/A189807/b189807.txt">Table of n, a(n) for n = 1..200</a> %F A189807 Empirical: a(n) = 6*n^2 + 26*n - 42 for n>3. %F A189807 Conjectures from _Colin Barker_, May 03 2018: (Start) %F A189807 G.f.: 2*x*(7 + x + 2*x^2 - 3*x^3 + x^4 - 2*x^5) / (1 - x)^3. %F A189807 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6. %F A189807 (End) %e A189807 Some solutions for n=3: %e A189807 ..3..0....0..1....2..1....1..1....2..0....3..0....1..1....2..2....0..0....3..1 %e A189807 ..0..0....0..0....1..0....0..1....2..1....2..0....0..2....1..1....0..2....1..1 %e A189807 ..3..1....3..1....3..0....1..2....3..0....3..2....2..2....3..1....3..0....3..2 %Y A189807 Cf. A189814. %K A189807 nonn %O A189807 1,1 %A A189807 _R. H. Hardin_, Apr 28 2011