A194816 - OEIS

A194816

Number of integers k in [1,n] such that {n*r+k*r} > {n*r-k*r}, where { } = fractional part and r=sqrt(2).

1, 1, 1, 2, 3, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 7, 8, 9, 9, 9, 10, 11, 12, 12, 12, 12, 13, 14, 15, 16, 16, 16, 17, 18, 19, 19, 19, 19, 20, 21, 21, 21, 21, 21, 22, 23, 24, 24, 24, 24, 25, 26, 26, 26, 26, 27, 28, 29, 30, 30, 30, 31, 32, 33, 33, 33, 33, 34, 35, 35, 35, 35, 35

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OFFSET

1,4

LINKS

Table of n, a(n) for n=1..73.

MATHEMATICA

r = Sqrt[2]; 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}] (* A194815 *)