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 A194319 Triangular array:  g(n,k)=number of fractional parts (i*sqrt(8)) in interval [(k-1)/n, k/n], for 1<=i<=n^2, 1<=k<=n. 2
 1, 2, 2, 2, 4, 3, 2, 6, 3, 5, 4, 5, 5, 6, 5, 6, 5, 6, 6, 7, 6, 7, 6, 6, 7, 8, 8, 7, 8, 8, 8, 8, 8, 8, 7, 9, 8, 9, 10, 7, 10, 10, 8, 10, 9, 9, 11, 9, 11, 9, 11, 8, 12, 9, 11, 9, 11, 11, 12, 11, 11, 11, 10, 12, 11, 12, 12, 12, 11, 13, 11, 13, 11, 13, 11, 13, 12, 12, 13, 13, 13, 13 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See A194285. LINKS EXAMPLE First nine rows: 1 2...2 2...4...3 2...6...3...5 4...5...5...6...5 6...5...6...6...7...6 7...6...6...7...8...8...7 8...8...8...8...8...8...7...9 8...9...10..7...10..10..8...10...9 MATHEMATICA r = Sqrt[8]; 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[%]    (* A194319 *) CROSSREFS Cf. A194285. Sequence in context: A121806 A056944 A222819 * A208609 A050493 A085454 Adjacent sequences:  A194316 A194317 A194318 * A194320 A194321 A194322 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Aug 22 2011 STATUS approved

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