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 A194289 #5 Mar 30 2012 18:57:42 %S A194289 1,1,1,1,1,1,1,1,1,1,1,0,1,2,1,0,1,2,1,1,1,1,1,1,1,1,1,1,1,1,0,2,0,2, %T A194289 1,1,0,2,0,1,1,2,1,1,1,0,2,0,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, %U A194289 1,1,1,1,0,2,1,1,1,1,1,1,1,0,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1 %N A194289 Triangular array: g(n,k)=number of fractional parts (i*sqrt(3)) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=n. %C A194289 See A194285. %e A194289 First eight rows: %e A194289 1 %e A194289 1..1 %e A194289 1..1..1 %e A194289 1..1..1..1 %e A194289 1..0..1..2..1 %e A194289 0..1..2..1..1..1 %e A194289 1..1..1..1..1..1..1 %e A194289 1..1..0..2..0..2..1..1 %t A194289 r = Sqrt[3]; %t A194289 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0] %t A194289 g[n_, k_] := Sum[f[n, k, i], {i, 1, n}] %t A194289 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]] %t A194289 Flatten[%] (* A194289 *) %Y A194289 Cf. A194285. %K A194289 nonn,tabl %O A194289 1,14 %A A194289 _Clark Kimberling_, Aug 21 2011