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 A243612 Irregular triangular array of numerators of all rational numbers ordered as in Comments. 5
 0, -1, 1, -1, 2, -2, -1, 1, 3, -3, -2, -1, 2, 3, 4, -3, -4, -3, -2, -1, 1, 3, 5, 5, 5, -5, -5, -5, -3, -4, -3, -2, -1, 2, 3, 4, 4, 7, 8, 7, 6, -4, -7, -8, -7, -6, -5, -5, -5, -3, -4, -3, -2, -1, 1, 3, 5, 5, 5, 7, 8, 9, 7, 11, 11, 9, 7, -7, -8, -9, -7, -11 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Let F = A000045 (the Fibonacci numbers).  Row n of the array to be generated consists of F(n-1) nonnegative rationals together with F(n-1) negative rationals.  The nonnegatives, for n >=3, are x + 1 from the F(n-2) nonnegative numbers x in row n-1, together with x/(x + 1) from the F(n-3) nonnegative numbers x in row n-2.  The negatives in row n are the negative reciprocals of the positives in row n. LINKS Clark Kimberling, Table of n, a(n) for n = 1..3000 EXAMPLE First 6 rows of the array of all rationals: 0/1 -1/1 .. 1/1 -1/2 .. 2/1 -2/1 .. -1/3 .. 1/2 ... 3/1 -3/2 .. -2/3 .. -1/4 .. 2/3 ... 3/2 ... 4/1 -3/1 .. -4/3 .. -3/5 .. -2/5 .. -1/5 .. 1/3 . 3/4 . 5/3 . 5/2 . 5/1 The numerators, by rows:  0,-1, 1, -1, 2, -2, -1, 1, 3, -3, -2, -1, 2, 3, 4, -2, -4, -3, -2, -1, 1,3,5,5,5,... MATHEMATICA z = 12; g[1] = {0}; f1[x_] := x + 1; f2[x_] := -1/(x + 1); h[1] = g[1]; b[n_] := b[n] = DeleteDuplicates[Union[f1[g[n - 1]], f2[g[n - 1]]]]; h[n_] := h[n] = Union[h[n - 1], g[n - 1]]; g[n_] := g[n] = Complement [b[n], Intersection[b[n], h[n]]] u = Table[g[n], {n, 1, z}] v = Table[Reverse[Drop[g[n], Fibonacci[n - 1]]], {n, 2, z}] Delete[Flatten[Denominator[u]], 6]  (* A243611 *) Delete[Flatten[Numerator[u]], 6]    (* A243612 *) Delete[Flatten[Denominator[v]], 2]  (* A243613 *) Delete[Flatten[Numerator[v]], 2]    (* A243614 *) ListPlot[g[20]] CROSSREFS Cf. A243611, A243613, A243614, A226131, A000045. Sequence in context: A126081 A268507 A272351 * A230351 A102481 A231201 Adjacent sequences:  A243609 A243610 A243611 * A243613 A243614 A243615 KEYWORD easy,tabf,frac,sign AUTHOR Clark Kimberling, Jun 08 2014 STATUS approved

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Last modified September 21 07:08 EDT 2019. Contains 327253 sequences. (Running on oeis4.)