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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=(1+sqrt(3))/2.
2

%I #5 Mar 30 2012 18:57:42

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

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

%U 11,11,11,11,11,11,11,13,12,11,13,12,12,11,13,12,12,12,13,14,13

%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=(1+sqrt(3))/2.

%C See A194285.

%e First eight rows:

%e 1

%e 3..1

%e 3..3..3

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

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

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

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

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

%t r = (1+Sqrt[3])/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[%] (* A194299 *)

%Y Cf. A194285.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Aug 21 2011