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 A194675 Triangular array: T(n,k)=[+], where [ ] = floor, < > =  fractional part. 5
 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 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 A194676. LINKS EXAMPLE First ten rows: 1 1 0 0 0 0 1 0 0 1 1 0 0 1 0 1 0 0 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 MATHEMATICA r = E; 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}]] (* A194675 *) TableForm[Table[w[n, k], {n, 1, z}, {k, 1, n}]] s[n_] := Sum[w[n, k], {k, 1, n}]  (* A194676 *) 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}]] (* A194677 *) 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}]  (* A194678 *) CROSSREFS Cf. A194676. Sequence in context: A218171 A232714 A274179 * A117964 A179020 A179771 Adjacent sequences:  A194672 A194673 A194674 * A194676 A194677 A194678 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Sep 01 2011 STATUS approved

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Last modified September 19 04:52 EDT 2019. Contains 327187 sequences. (Running on oeis4.)