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.

A194301 Triangular array: g(n,k)=number of fractional parts (i*sqrt(5)) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=n.

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%I A194301 #6 Mar 30 2012 18:57:42
%S A194301 1,2,0,1,1,1,1,1,1,1,1,1,1,1,1,0,2,2,0,1,1,0,2,1,1,2,0,1,0,2,0,2,0,2,
%T A194301 0,2,0,2,1,1,1,1,1,1,1,0,2,1,1,2,0,1,1,1,1,0,2,1,1,1,1,1,2,0,1,1,0,1,
%U A194301 2,0,2,1,0,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,0
%N A194301 Triangular array:  g(n,k)=number of fractional parts (i*sqrt(5)) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=n.
%C A194301 See A194285.
%e A194301 First nine rows:
%e A194301 1
%e A194301 2..0
%e A194301 1..1..1
%e A194301 1..1..1..1
%e A194301 1..1..1..1..1
%e A194301 0..2..2..0..1..1
%e A194301 0..2..1..1..2..0..1
%e A194301 0..2..0..2..0..2..0..2
%e A194301 0..2..1..1..1..1..1..1..1
%t A194301 r = Sqrt[5];
%t A194301 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t A194301 g[n_, k_] := Sum[f[n, k, i], {i, 1, n}]
%t A194301 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t A194301 Flatten[%]    (* A194301 *)
%Y A194301 Cf. A194285.
%K A194301 nonn,tabl
%O A194301 1,2
%A A194301 _Clark Kimberling_, Aug 21 2011