cp's OEIS Frontend

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.

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.

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%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