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.

A194294 Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=2n, r=(1+sqrt(5))/2, the golden ratio.

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%I A194294 #5 Mar 30 2012 18:57:42
%S A194294 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,3,2,2,2,2,2,2,2,2,3,2,1,2,2,2,2,2,2,
%T A194294 2,2,2,2,3,1,2,3,1,3,1,2,2,2,2,2,2,2,3,2,1,2,2,2,2,1,2,3,2,2,2,2,1,2,
%U A194294 3,2,2,1,2,3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,3,2,2,2,2
%N A194294 Triangular array:  g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=2n, r=(1+sqrt(5))/2, the golden ratio.
%C A194294 See A194285.
%e A194294 First nine rows:
%e A194294 2
%e A194294 2..2
%e A194294 2..2..2
%e A194294 2..2..2..2
%e A194294 2..2..2..2..2
%e A194294 1..3..2..2..2..2
%e A194294 2..2..2..2..3..2..1
%e A194294 2..2..2..2..2..2..2..2
%e A194294 2..2..3..1..2..3..1..3..1
%t A194294 r = GoldenRatio;
%t A194294 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t A194294 g[n_, k_] := Sum[f[n, k, i], {i, 1, 2n}]
%t A194294 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t A194294 Flatten[%]    (* A194294 *)
%Y A194294 Cf. A194285, A194293.
%K A194294 nonn,tabl
%O A194294 1,1
%A A194294 _Clark Kimberling_, Aug 21 2011