A194748 - OEIS

A194748

Number of k such that {-k*sqrt(6)} < {-n*sqrt(6)}, where { } = fractional part.

1, 1, 3, 2, 5, 3, 7, 4, 9, 5, 1, 8, 3, 11, 5, 14, 7, 17, 9, 1, 13, 4, 17, 7, 21, 10, 25, 13, 29, 16, 3, 21, 7, 26, 11, 31, 15, 36, 19, 2, 25, 7, 31, 12, 37, 17, 43, 22, 49, 27, 5, 34, 11, 41, 17, 48, 23, 55, 29, 3, 37, 10, 45, 17, 53, 24, 61, 31, 69, 38, 7, 47, 15, 56, 23

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OFFSET

1,3

LINKS

Table of n, a(n) for n=1..75.

MATHEMATICA

r = -Sqrt[6]; p[x_] := FractionalPart[x];

u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]

v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]

s[n_] := Sum[u[n, k], {k, 1, n}]

t[n_] := Sum[v[n, k], {k, 1, n}]

Table[s[n], {n, 1, 100}] (* A194748 *)