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 A194294 #5 Mar 30 2012 18:57:42 %S A194294 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,3,2,2,2,2,2,2,2,2,3,2,1,2,2,2,2,2,2, %T A194294 2,2,2,2,3,1,2,3,1,3,1,2,2,2,2,2,2,2,3,2,1,2,2,2,2,1,2,3,2,2,2,2,1,2, %U A194294 3,2,2,1,2,3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,3,2,2,2,2 %N A194294 Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=2n, r=(1+sqrt(5))/2, the golden ratio. %C A194294 See A194285. %e A194294 First nine rows: %e A194294 2 %e A194294 2..2 %e A194294 2..2..2 %e A194294 2..2..2..2 %e A194294 2..2..2..2..2 %e A194294 1..3..2..2..2..2 %e A194294 2..2..2..2..3..2..1 %e A194294 2..2..2..2..2..2..2..2 %e A194294 2..2..3..1..2..3..1..3..1 %t A194294 r = GoldenRatio; %t A194294 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0] %t A194294 g[n_, k_] := Sum[f[n, k, i], {i, 1, 2n}] %t A194294 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]] %t A194294 Flatten[%] (* A194294 *) %Y A194294 Cf. A194285, A194293. %K A194294 nonn,tabl %O A194294 1,1 %A A194294 _Clark Kimberling_, Aug 21 2011