login
A194817
Number of integers k in [1,n] such that {n*r+k*r} < {n*r-k*r}, where { } = fractional part and r=sqrt(3).
2
0, 1, 1, 2, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 8, 9, 9, 10, 11, 12, 12, 12, 13, 13, 13, 13, 14, 14, 15, 16, 17, 17, 18, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21, 22, 23, 24, 24, 25, 26, 26, 26, 26, 27, 27, 28, 29, 30, 30, 31, 32, 33, 33, 33, 34, 34, 34, 34, 35, 35, 36, 37
OFFSET
1,4
MATHEMATICA
r = Sqrt[3]; p[x_] := FractionalPart[x];
u[n_, k_] := If[p[n*r + k*r] <= p[n*r - k*r], 1, 0]
v[n_, k_] := If[p[n*r + k*r] > p[n*r - k*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}] (* A194817 *)
Table[t[n], {n, 1, 100}] (* A194818 *)
CROSSREFS
Partial sums of A327180.
Sequence in context: A130245 A087793 A030411 * A211675 A239683 A132913
KEYWORD
nonn
AUTHOR
Clark Kimberling, Sep 03 2011
STATUS
approved