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 A194681 Triangular array: T(n,k)=[+], where [ ] = floor, < > =  fractional part, and r=3-sqrt(2). 4
 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1 COMMENTS n-th row sum gives number of k in [0,1] for which + > 1; see A194678. LINKS G. C. Greubel, Table of n, a(n) for the first 150 rows, flattened EXAMPLE First ten rows: 1 0 0 1 0 1 0 0 1 0 1 1 1 1 1 1 0 1 0 1 1 0 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 0 1 0 1 0 0 0 0 1 1 1 1 1 1 0 1 1 1 MATHEMATICA r = 3 - Sqrt[2]; z = 15; p[x_] := FractionalPart[x]; f[x_] := Floor[x]; w[n_, k_] := p[r^n] + p[r^k] - p[r^n + r^k] Flatten[Table[w[n, k], {n, 1, z}, {k, 1, n}]]   (* A194679 *) TableForm[Table[w[n, k], {n, 1, z}, {k, 1, n}]] s[n_] := Sum[w[n, k], {k, 1, n}]  (* A194680 *) Table[s[n], {n, 1, 100}] h[n_, k_] := f[p[n*r] + p[k*r]] Flatten[Table[h[n, k], {n, 1, z}, {k, 1, n}]]   (* A194681 *) TableForm[Table[h[n, k], {n, 1, z}, {k, 1, n}]] t[n_] := Sum[h[n, k], {k, 1, n}] Table[t[n], {n, 1, 100}]   (* A194682 *) PROG (PARI) for(n=1, 10, for(k=1, n, print1(floor(frac(n*(3-sqrt(2))) + frac(k*(3-sqrt(2)))), ", "))) \\ G. C. Greubel, Feb 08 2018 CROSSREFS Cf. A194682. Sequence in context: A232990 A285076 A267598 * A065043 A189298 A288375 Adjacent sequences:  A194678 A194679 A194680 * A194682 A194683 A194684 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Sep 01 2011 STATUS approved

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Last modified September 19 10:57 EDT 2019. Contains 327192 sequences. (Running on oeis4.)