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 A194305 #9 Apr 10 2021 08:04:17 %S A194305 1,2,0,2,1,0,1,2,1,0,1,1,2,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,2,1,1,1,1, %T A194305 1,1,0,2,2,1,0,1,1,1,1,0,2,2,0,2,1,0,1,1,1,0,2,0,2,2,0,2,1,0,1,1,0,2, %U A194305 0,2,1,1,2,0,2,0,1,1,0,2,0,2,0,2,0,2,0,2,1,1,1,0,2,0,2,0,2,0,2 %N A194305 Triangular array: g(n,k) = number of fractional parts (i*Pi) in interval [(k-1)/n, k/n], for 1 <= i <= n, 1 <= k <= n. %C A194305 See A194285. %e A194305 First eleven rows: %e A194305 1; %e A194305 2, 0; %e A194305 2, 1, 0; %e A194305 1, 2, 1, 0; %e A194305 1, 1, 2, 1, 0; %e A194305 1, 1, 1, 1, 1, 1; %e A194305 1, 1, 1, 1, 1, 1, 1; %e A194305 0, 2, 1, 1, 1, 1, 1, 1; %e A194305 0, 2, 2, 1, 0, 1, 1, 1, 1; %e A194305 0, 2, 2, 0, 2, 1, 0, 1, 1, 1; %e A194305 0, 2, 0, 2, 2, 0, 2, 1, 0, 1, 1; %t A194305 r = Pi; %t A194305 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0] %t A194305 g[n_, k_] := Sum[f[n, k, i], {i, 1, n}] %t A194305 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]] %t A194305 Flatten[%] (* A194305 *) %Y A194305 Cf. A194285. %K A194305 nonn,tabl %O A194305 1,2 %A A194305 _Clark Kimberling_, Aug 21 2011