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 A194341 #5 Mar 30 2012 18:57:43 %S A194341 1,1,1,1,1,1,1,1,1,1,1,1,2,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,2,1,1,1, %T A194341 1,1,0,1,2,1,1,1,1,1,1,0,1,2,0,1,2,1,0,2,1,0,2,1,1,1,1,1,1,1,1,1,0,2, %U A194341 0,2,2,0,2,0,1,1,1,1,0,2,0,2,1,1,1,1,2,0,2,0,1,0,2,0,2,0,2,0,2,0 %N A194341 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-e. %C A194341 See A194285. %e A194341 First ten rows: %e A194341 1 %e A194341 1..1 %e A194341 1..1..1 %e A194341 1..1..1..1 %e A194341 1..1..2..0..1 %e A194341 1..1..1..1..1..1 %e A194341 1..1..1..1..1..1..1 %e A194341 0..1..2..1..1..1..1..1 %e A194341 0..1..2..0..1..2..1..0..2..1 %t A194341 r = 3-E; %t A194341 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0] %t A194341 g[n_, k_] := Sum[f[n, k, i], {i, 1, n}] %t A194341 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]] %t A194341 Flatten[%] (* A194341 *) %Y A194341 Cf. A193285. %K A194341 nonn,tabl %O A194341 1,13 %A A194341 _Clark Kimberling_, Aug 22 2011