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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

%I

%S 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,

%T 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,

%U 11,10,12,11,12,12,12,11,13,11,13,11,13,11,13,12,12,13,13,13,13

%N 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.

%C See A194285.

%e First nine rows:

%e 1

%e 2...2

%e 2...4...3

%e 2...6...3...5

%e 4...5...5...6...5

%e 6...5...6...6...7...6

%e 7...6...6...7...8...8...7

%e 8...8...8...8...8...8...7...9

%e 8...9...10..7...10..10..8...10...9

%t r = Sqrt[8];

%t f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]

%t g[n_, k_] := Sum[f[n, k, i], {i, 1, n^2}]

%t TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]

%t Flatten[%] (* A194319 *)

%Y Cf. A194285.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Aug 22 2011

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Last modified June 16 08:46 EDT 2021. Contains 345056 sequences. (Running on oeis4.)