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A194327 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(2). 2

%I

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

%T 7,9,9,9,9,9,9,9,10,9,8,9,10,10,10,10,11,10,10,10,10,10,12,11,11,11,

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

%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(2).

%C See A194285.

%e First eight rows:

%e 1

%e 2..2

%e 3..3..3

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

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

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

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

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

%t r = 2-Sqrt[2];

%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[%] (* A194327 *)

%Y Cf. A194285.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Aug 22 2011

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Last modified October 20 03:04 EDT 2021. Contains 348099 sequences. (Running on oeis4.)