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 A194679 Triangular array: T(n,k)=[+], where [ ] = floor, < > =  fractional part, and r=3-sqrt(2). 5
 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1 (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 A194680. LINKS G. C. Greubel, Table of n, a(n) for the first 150 rows, flattened EXAMPLE First ten rows: 1 1 1 1 1 1 0 0 1 0 0 0 1 0 0 1 1 1 1 0 1 0 0 1 0 0 1 0 1 1 1 1 1 1 1 1 1 0 1 0 0 1 0 1 0 1 1 1 0 0 1 0 1 0 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, 20, for(k=1, n, print1(round(frac((3-sqrt(2))^n) + frac((3-sqrt(2))^k) - frac((3-sqrt(2))^n + (3-sqrt(2))^k)), ", "))) \\ G. C. Greubel, Feb 08 2018 CROSSREFS Cf. A194679. Sequence in context: A174856 A175608 A285467 * A111940 A129572 A070950 Adjacent sequences:  A194676 A194677 A194678 * A194680 A194681 A194682 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Sep 01 2011 STATUS approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)