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 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). 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS 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 *) Table[t[n], {n, 1, 100}] (* A194816 *) CROSSREFS Cf. A194815, A194813. Sequence in context: A189660 A194167 A140427 * A178770 A072229 A120509 Adjacent sequences: A194813 A194814 A194815 * A194817 A194818 A194819 KEYWORD nonn AUTHOR Clark Kimberling, Sep 03 2011 STATUS approved

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Last modified February 4 12:59 EST 2023. Contains 360055 sequences. (Running on oeis4.)