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 A194815 Number of integers k in [1,n] such that {n*r+k*r} < {n*r-k*r}, where { } = fractional part and r=sqrt(2). 2

%I

%S 0,1,2,2,2,2,3,4,5,5,5,6,7,8,9,9,9,9,10,11,11,11,11,12,13,14,14,14,14,

%T 14,15,16,16,16,16,17,18,19,19,19,20,21,22,23,23,23,23,24,25,26,26,26,

%U 27,28,29,29,29,29,29,30,31,31,31,31,32,33,34,34,34,35,36,37

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

%t r = Sqrt[2]; p[x_] := FractionalPart[x];

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

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

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

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

%t Table[s[n], {n, 1, 100}] (* A194815 *)

%t Table[t[n], {n, 1, 100}] (* A194816 *)

%Y Cf. A002193, A194816, A194813.

%Y Partial sums of A327177.

%K nonn

%O 1,3

%A _Clark Kimberling_, Sep 03 2011

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Last modified March 24 18:34 EDT 2023. Contains 361510 sequences. (Running on oeis4.)