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 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. 3
 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, 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, 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,26 COMMENTS See A194285.  Which rows are constant? LINKS EXAMPLE First ten rows: 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..1..1 1..0..2..0..1..2..1..1..1 1..1..1..1..1..1..1..1..1..1 MATHEMATICA r = GoldenRatio; f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0] g[n_, k_] := Sum[f[n, k, i], {i, 1, n}] TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]] Flatten[%]    (* A194293 *) CROSSREFS Cf. A194293. Sequence in context: A073484 A203947 A081396 * A298941 A317146 A194297 Adjacent sequences:  A194290 A194291 A194292 * A194294 A194295 A194296 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Aug 21 2011 STATUS approved

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Last modified May 11 15:11 EDT 2021. Contains 343791 sequences. (Running on oeis4.)