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A194331 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-sqrt(3). 2

%I

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

%T 8,8,10,9,8,10,9,9,9,9,8,10,9,11,10,9,11,10,10,10,10,11,11,11,12,11,

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

%N Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n^2, 1<=k<=n, r=2-sqrt(3).

%C See A194285.

%e First eight rows:

%e 1

%e 2..2

%e 3..4..2

%e 4..5..3..4

%e 5..5..5..5..5

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

%e 7..7..7..7..7..7..7

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

%t r = 2-Sqrt[3];

%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[%] (* A194331 *)

%Y Cf. A194285.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Aug 22 2011

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Last modified October 23 22:28 EDT 2019. Contains 328373 sequences. (Running on oeis4.)