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

%I #5 Mar 30 2012 18:57:43

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

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

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

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

%C See A194285.

%e First eight rows:

%e 1

%e 2..2

%e 2..4..3

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

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

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

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

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

%t r = Sqrt[1/2];

%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[%] (* A194323 *)

%Y Cf. A194285.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Aug 22 2011