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 A194335 Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n^2, 1<=k<=n, r=2-tau, where tau=(1+sqrt(5))/2, the golden ratio. 2
 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6, 5, 4, 5, 6, 7, 5, 7, 6, 6, 7, 8, 7, 6, 8, 7, 8, 8, 8, 9, 7, 8, 8, 8, 8, 10, 8, 10, 9, 9, 9, 9, 9, 10, 10, 11, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 12, 11, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See A194285. LINKS Table of n, a(n) for n=1..81. EXAMPLE First eight rows: 1 2..2 3..3..3 4..4..4..4 5..5..6..5..4 5..6..7..5..7..6 6..7..8..7..6..8..7 8..8..8..9..7..8..8..8 MATHEMATICA r = 2-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^2}] TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]] Flatten[%] (* A194335 *) CROSSREFS Cf. A194285. Sequence in context: A056155 A157684 A194339 * A026099 A049727 A260690 Adjacent sequences: A194332 A194333 A194334 * A194336 A194337 A194338 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Aug 22 2011 STATUS approved

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Last modified April 19 21:09 EDT 2024. Contains 371798 sequences. (Running on oeis4.)