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 A194306 #9 Apr 10 2021 08:04:24 %S A194306 2,3,1,2,2,2,2,2,2,2,2,2,3,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,3,2,2,2, %T A194306 2,2,0,3,3,3,1,2,2,2,2,0,3,3,0,3,3,2,1,3,2,0,4,1,2,3,0,3,3,0,3,3,0,4, %U A194306 0,4,3,1,3,0,3,1,2,3,0,4,0,4,0,4,0,4,2,2,2,1,3,0,4,0,4,0,4,0,4,0 %N A194306 Triangular array: g(n,k) = number of fractional parts (i*Pi) in interval [(k-1)/n, k/n], for 1 <= i <= 2n, 1 <= k <= n. %C A194306 See A194285. %e A194306 First nine rows: %e A194306 3; %e A194306 3, 1; %e A194306 2, 2, 2; %e A194306 2, 2, 2, 2; %e A194306 2, 2, 3, 1, 2; %e A194306 2, 2, 2, 2, 2, 2; %e A194306 2, 2, 2, 2, 2, 2, 2; %e A194306 1, 2, 3, 2, 2, 2, 2, 2; %e A194306 0, 3, 3, 3, 1, 2, 2, 2, 2; %t A194306 r = Pi; %t A194306 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0] %t A194306 g[n_, k_] := Sum[f[n, k, i], {i, 1, n}] %t A194306 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]] %t A194306 Flatten[%] (* A194305 *) %Y A194306 Cf. A194285. %K A194306 nonn,tabl %O A194306 1,1 %A A194306 _Clark Kimberling_, Aug 21 2011