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 A194317 #5 Mar 30 2012 18:57:42 %S A194317 1,0,2,0,2,1,0,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,2,1,0,1,1,1,0,2, %T A194317 2,1,0,1,1,0,2,2,0,2,1,0,1,1,1,2,0,2,1,1,1,0,2,0,2,0,2,1,1,1,1,1,0,2, %U A194317 0,2,0,2,0,2,0,2,0,2,0,2,0,1,1,1,1,0,2,0,3,0,2,0,2,0,1,1,0,2,0 %N A194317 Triangular array: g(n,k)=number of fractional parts (i*sqrt(8)) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=n. %C A194317 See A194285. %e A194317 First eight rows: %e A194317 1 %e A194317 0..2 %e A194317 0..2..1 %e A194317 0..2..1..1 %e A194317 1..1..1..1..1 %e A194317 1..1..1..1..1..1 %e A194317 1..0..1..1..1..2..1 %e A194317 0..1..1..1..0..2..2..1 %t A194317 r = Sqrt[8]; %t A194317 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0] %t A194317 g[n_, k_] := Sum[f[n, k, i], {i, 1, n}] %t A194317 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]] %t A194317 Flatten[%] (* A194317 *) %Y A194317 Cf. A194285. %K A194317 nonn,tabl %O A194317 1,3 %A A194317 _Clark Kimberling_, Aug 22 2011