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 A194670 Triangular array: T(n,k)=[+], where [ ] = floor, < > =  fractional part, and r = sqrt(5). 3
 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 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 A194671. LINKS EXAMPLE First thirteen rows: 0 0 0 0 1 1 1 1 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 0 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 MATHEMATICA r = Sqrt[5]; 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}]  (* A194669 *) 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}]] (* A194670 *) 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}]  (* A194671 *) CROSSREFS Cf. A194671. Sequence in context: A091247 A085137 A304577 * A130543 A193243 A281302 Adjacent sequences:  A194667 A194668 A194669 * A194671 A194672 A194673 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Sep 01 2011 STATUS approved

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Last modified September 25 20:01 EDT 2020. Contains 337344 sequences. (Running on oeis4.)