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A194295 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^2, r=(1+sqrt(5))/2, the golden ratio. 2

%I

%S 1,2,2,3,3,3,4,4,4,4,4,5,6,5,5,6,7,5,7,6,5,7,8,6,7,8,7,6,8,8,8,7,9,8,

%T 8,8,9,9,9,9,9,10,8,10,8,10,10,10,10,10,10,9,11,10,10,11,11,11,11,10,

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

%N 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^2, r=(1+sqrt(5))/2, the golden ratio.

%C See A194285.

%e First eight rows:

%e 1

%e 2..2

%e 3..3..3

%e 4..4..4..4

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

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

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

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

%t r = GoldenRatio;

%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[%] (* A194295 *)

%Y Cf. A194295.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Aug 21 2011

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Last modified May 11 16:48 EDT 2021. Contains 343805 sequences. (Running on oeis4.)