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 A189809 #9 May 03 2018 07:02:54 %S A189809 46,158,342,596,926,1308,1754,2250,2794,3390,4026,4702,5426,6190,6994, %T A189809 7838,8726,9654,10622,11630,12678,13766,14894,16062,17270,18518,19806, %U A189809 21134,22502,23910,25358,26846,28374,29942,31550,33198,34886,36614,38382 %N A189809 Number of right triangles on an (n+1) X 5 grid. %C A189809 Column 4 of A189814. %H A189809 R. H. Hardin, <a href="/A189809/b189809.txt">Table of n, a(n) for n = 1..200</a> %F A189809 Empirical: a(n) = 20*n^2 + 228*n - 930 for n>15. %F A189809 Conjectures from _Colin Barker_, May 03 2018: (Start) %F A189809 G.f.: 2*x*(23 + 10*x + 3*x^2 - x^3 + 3*x^4 - 12*x^5 + 6*x^6 - 7*x^7 - x^8 + 2*x^9 - 6*x^10 + 4*x^12 - 4*x^13 + 2*x^16 - 2*x^17) / (1 - x)^3. %F A189809 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>11. %F A189809 (End) %e A189809 Some solutions for n=3: %e A189809 ..1..4....3..3....3..3....3..3....1..2....2..0....3..2....0..3....3..2....0..1 %e A189809 ..0..4....0..3....1..3....1..1....2..1....0..1....0..2....0..2....2..2....0..0 %e A189809 ..1..0....3..4....3..0....2..4....3..4....3..2....3..3....1..3....3..3....3..1 %Y A189809 Cf. A189814. %K A189809 nonn %O A189809 1,1 %A A189809 _R. H. Hardin_, Apr 28 2011