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 A194661 Triangular array: T(n,k)=[+], where [ ] = floor, < > =  fractional part, and r = (1+sqrt(5))/2 (the golden ratio). 2
 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1 COMMENTS n-th row sum gives the number of k in [0,n] for which + > 1; see A194662. Triangles of this sort and their row sums are sampled by the following sequences: A194661-A194662: r=(1+sqrt(5))/2 A194663-A194665: r=sqrt(2) A194666-A194668: r=sqrt(3) A194669-A194671: r=sqrt(5) A194675-A194678: r=e A194679-A194682: r=3-sqrt(2) A194683-A194686: r=(1+sqrt(3))/2 LINKS EXAMPLE First 13 rows: 1 0 0 1 1 1 1 0 1 0 0 0 0 0 0 1 0 1 1 0 1 0 0 1 0 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 0 0 1 0 0 0 0 1 0 0 1 1 1 1 0 1 1 1 1 0 1 1 0 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 MATHEMATICA r = GoldenRatio; z = 14; p[x_] := FractionalPart[x]; f[x_] := Floor[x]; h[n_, k_] := f[p[n*r] + p[k*r]] Flatten[Table[h[n, k], {n, 1, z}, {k, 1, n}]] (* A194661 *) 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}]   (* A194662 *) CROSSREFS Cf. A194662. Sequence in context: A071674 A090172 A284369 * A285427 A285621 A204435 Adjacent sequences:  A194658 A194659 A194660 * A194662 A194663 A194664 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Sep 01 2011 STATUS approved

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Last modified July 28 17:07 EDT 2021. Contains 346335 sequences. (Running on oeis4.)