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 A194337 #5 Mar 30 2012 18:57:43 %S A194337 1,0,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,2,2,0,1,0,2,1,1,2,0,2,0,2,0,2,0, %T A194337 2,0,1,1,1,1,1,1,1,2,0,1,1,1,1,0,2,1,1,2,0,1,1,0,2,1,1,1,1,1,2,0,1,1, %U A194337 1,1,2,0,1,2,0,2,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,2,1,0,1 %N A194337 Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=n, r=3-sqrt(5). %C A194337 See A194285. %e A194337 First nine rows: %e A194337 1 %e A194337 0..2 %e A194337 1..1..1 %e A194337 1..1..1..1 %e A194337 1..1..1..1..1 %e A194337 1..1..0..2..2..0 %e A194337 1..0..2..1..1..2..0 %e A194337 2..0..2..0..2..0..2..0 %e A194337 1..1..1..1..1..1..1..2..0 %t A194337 r = 3-Sqrt[5]; %t A194337 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0] %t A194337 g[n_, k_] := Sum[f[n, k, i], {i, 1, n}] %t A194337 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]] %t A194337 Flatten[%] (* A194337 *) %Y A194337 Cf. A194285. %K A194337 nonn,tabl %O A194337 1,3 %A A194337 _Clark Kimberling_, Aug 22 2011