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 A194664 Triangular array: T(n,k)=[+], where [ ] = floor, < > =  fractional part, and r = sqrt(2). 3
 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 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 A194665. LINKS G. C. Greubel, Table of n, a(n) for the first 150 rows, flattened EXAMPLE First thirteen rows: 0 1 1 0 1 0 1 1 0 1 0 0 0 0 0 0 1 0 1 0 0 1 1 1 1 0 1 1 0 1 0 0 0 0 1 0 1 1 0 1 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 0 1 0 1 0 0 1 0 MATHEMATICA r = Sqrt[2]; z = 13; 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}]] TableForm[Table[w[n, k], {n, 1, z}, {k, 1, n}]] s[n_] := Sum[w[n, k], {k, 1, n}]  (* A194663 *) 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}]] (* A194664 *) 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}]    (* A194665 *) CROSSREFS Cf. A194665. Sequence in context: A284653 A099104 A066829 * A285975 A213729 A296135 Adjacent sequences:  A194661 A194662 A194663 * A194665 A194666 A194667 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Sep 01 2011 STATUS approved

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Last modified July 26 15:49 EDT 2021. Contains 346294 sequences. (Running on oeis4.)