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.

A194293 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=(1+sqrt(5))/2, the golden ratio.

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%I A194293 #5 Mar 30 2012 18:57:42
%S A194293 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,0,1,1,1,1,1,1,
%T A194293 1,1,1,0,2,0,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,2,1,1,1,1,0,1,
%U A194293 2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N A194293 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=(1+sqrt(5))/2, the golden ratio.
%C A194293 See A194285.  Which rows are constant?
%e A194293 First ten rows:
%e A194293 1
%e A194293 1..1
%e A194293 1..1..1
%e A194293 1..1..1..1
%e A194293 1..1..1..1..1
%e A194293 1..1..1..1..1..1
%e A194293 1..1..1..1..2..1..0
%e A194293 1..1..1..1..1..1..1..1
%e A194293 1..0..2..0..1..2..1..1..1
%e A194293 1..1..1..1..1..1..1..1..1..1
%t A194293 r = GoldenRatio;
%t A194293 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t A194293 g[n_, k_] := Sum[f[n, k, i], {i, 1, n}]
%t A194293 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t A194293 Flatten[%]    (* A194293 *)
%Y A194293 Cf. A194293.
%K A194293 nonn,tabl
%O A194293 1,26
%A A194293 _Clark Kimberling_, Aug 21 2011